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Boost-Commit : |
Subject: [Boost-commit] svn:boost r76372 - in sandbox/math_constants: boost/math/constants libs/math/test
From: john_at_[hidden]
Date: 2012-01-08 13:22:25
Author: johnmaddock
Date: 2012-01-08 13:22:24 EST (Sun, 08 Jan 2012)
New Revision: 76372
URL: http://svn.boost.org/trac/boost/changeset/76372
Log:
Update calculations to honour the number of digits precision requested by the Policy in effect.
Update tests to test all the constants in all permutations: mostly cut and paste.
Text files modified:
sandbox/math_constants/boost/math/constants/calculate_constants.hpp | 97 +-----
sandbox/math_constants/libs/math/test/test_constants.cpp | 510 ++++++++++++++++++++++++++++++++++-----
2 files changed, 456 insertions(+), 151 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 2012-01-08 13:22:24 EST (Sun, 08 Jan 2012)
@@ -144,7 +144,8 @@
// Mathematics of Comnputation, Volume 34, Number 149, Jan 1980, pages 305-312.
// See equation 17 with p = 2.
//
- T n = 3 + boost::math::tools::digits<T>() / 4;
+ T n = 3 + (M ? (std::min)(M, tools::digits<T>()) : tools::digits<T>()) / 4;
+ T lim = M ? ldexp(T(1), (std::min)(M, tools::digits<T>())) : tools::epsilon<T>();
T lnn = log(n);
T term = 1;
T N = -lnn;
@@ -160,7 +161,7 @@
N += term * (Hk - lnn);
D += term;
- if(term < D * boost::math::tools::epsilon<T>())
+ if(term < D * lim)
break;
}
return N / D;
@@ -542,63 +543,6 @@
log((static_cast<T>(1) + sqrt(static_cast<T>(5)) )/static_cast<T>(2) );
}
-/*
-Gamma now deprecated, so now see euler above
-// Euler-Mascheroni's Gamma Constant
-
-//http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant
-
-//http://en.wikipedia.org/wiki/Gamma_function
-
-template <class T>
-template<int N>
-inline T constant_gamma<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
-{
- BOOST_MATH_STD_USING
- // 1000 digits from http://www.wolframalpha.com
- T gamma(
- "0.577215664901532860606512090082402431042159335939923598805767234884867726"
- "777664670936947063291746749514631447249807082480960504014486542836224173"
- "997644923536253500333742937337737673942792595258247094916008735203948165"
- "670853233151776611528621199501507984793745085705740029921354786146694029"
- "604325421519058775535267331399254012967420513754139549111685102807984234"
- "877587205038431093997361372553060889331267600172479537836759271351577226"
- "102734929139407984301034177717780881549570661075010161916633401522789358"
- "679654972520362128792265559536696281763887927268013243101047650596370394"
- "739495763890657296792960100901512519595092224350140934987122824794974719"
- "564697631850667612906381105182419744486783638086174945516989279230187739"
- "107294578155431600500218284409605377243420328547836701517739439870030237"
- "033951832869000155819398804270741154222781971652301107356583396734871765"
- "049194181230004065469314299929777956930310050308630341856980323108369164"
- "0025892970890985486825777364288253954925873629596133298574739302"
-);
- // T gamma("0.57721566490153286060651209008240243104215933593992");
- return gamma;
-
-}
-
-template <class T>
-template<int N>
-inline T constant_one_div_gamma<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
-{
- BOOST_MATH_STD_USING
-
- return static_cast<T>(1)
- / gamma<T, policies::policy<policies::digits2<N> > >();
-}
-
-
-
-template <class T>
-template<int N>
-inline T constant_gamma_sqr<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
-{
- BOOST_MATH_STD_USING
-
- return gamma<T, policies::policy<policies::digits2<N> > >()
- * gamma<T, policies::policy<policies::digits2<N> > >();
-}
-*/
// Zeta
template <class T>
@@ -636,7 +580,7 @@
T sum = static_cast<double>(77); // Start with n = 0 case.
// for n = 0, (77/1) /64 = 1.203125
//double lim = std::numeric_limits<double>::epsilon();
- T lim = boost::math::tools::epsilon<T>();
+ T lim = N ? ldexp(T(1), 1 - (std::min)(N, tools::digits<T>())) : tools::epsilon<T>();
for(unsigned int n = 1; n < 40; ++n)
{ // three to five decimal digits per term, so 40 should be plenty for 100 decimal digits.
//cout << "n = " << n << endl;
@@ -687,7 +631,7 @@
T tk_fact = 1;
T sum = 1;
T term;
- T lim = boost::math::tools::epsilon<T>();
+ T lim = N ? ldexp(T(1), 1 - (std::min)(N, tools::digits<T>())) : tools::epsilon<T>();
for(unsigned k = 1;; ++k)
{
@@ -709,7 +653,7 @@
namespace khinchin_detail{
template <class T>
-T zeta_polynomial_series(T s, T sc)
+T zeta_polynomial_series(T s, T sc, int digits)
{
BOOST_MATH_STD_USING
//
@@ -720,7 +664,7 @@
// See: http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf
//
BOOST_MATH_STD_USING
- int n = itrunc(T(log(boost::math::tools::epsilon<T>()) / -2));
+ int n = (digits * 19) / 53;
T sum = 0;
T two_n = ldexp(T(1), n);
int ej_sign = 1;
@@ -743,12 +687,12 @@
}
template <class T>
-T khinchin()
+T khinchin(int digits)
{
BOOST_MATH_STD_USING
T sum = 0;
T term;
- T lim = boost::math::tools::epsilon<T>();
+ T lim = ldexp(T(1), 1-digits);
T factor = 0;
unsigned last_k = 1;
T num = 1;
@@ -760,7 +704,7 @@
num = -num;
}
last_k = 2 * n;
- term = (zeta_polynomial_series(T(2 * n), T(1 - T(2 * n))) - 1) * factor / n;
+ term = (zeta_polynomial_series(T(2 * n), T(1 - T(2 * n)), digits) - 1) * factor / n;
sum += term;
if(term < lim)
break;
@@ -774,7 +718,8 @@
template<int N>
inline T constant_khinchin<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
- return khinchin_detail::khinchin<T>();
+ int n = N ? (std::min)(N, tools::digits<T>()) : tools::digits<T>();
+ return khinchin_detail::khinchin<T>(n);
}
template <class T>
@@ -818,11 +763,12 @@
// See http://www.math.utexas.edu/users/villegas/publications/conv-accel.pdf
//
template <class T>
-T zeta_series_derivative_2()
+T zeta_series_derivative_2(unsigned digits)
{
// Derivative of the series part, evaluated at 2:
BOOST_MATH_STD_USING
- int n = boost::math::itrunc((std::numeric_limits<T>::digits10 + 1) * 1.3);
+ int n = digits * 301 * 13 / 10000;
+ boost::math::itrunc((std::numeric_limits<T>::digits10 + 1) * 1.3);
T d = pow(3 + sqrt(T(8)), n);
d = (d + 1 / d) / 2;
T b = -1;
@@ -839,11 +785,11 @@
}
template <class T>
-T zeta_series_2()
+T zeta_series_2(unsigned digits)
{
// Series part of zeta at 2:
BOOST_MATH_STD_USING
- int n = boost::math::itrunc((std::numeric_limits<T>::digits10 + 1) * 1.3);
+ int n = digits * 301 * 13 / 10000;
T d = pow(3 + sqrt(T(8)), n);
d = (d + 1 / d) / 2;
T b = -1;
@@ -874,11 +820,11 @@
}
template <class T>
-inline T zeta_derivative_2()
+inline T zeta_derivative_2(unsigned n)
{
// zeta derivative at 2:
- return zeta_series_derivative_2<T>() * zeta_series_lead_2<T>()
- + zeta_series_derivative_lead_2<T>() * zeta_series_2<T>();
+ return zeta_series_derivative_2<T>(n) * zeta_series_lead_2<T>()
+ + zeta_series_derivative_lead_2<T>() * zeta_series_2<T>(n);
}
} // namespace detail
@@ -890,7 +836,8 @@
BOOST_MATH_STD_USING
typedef policies::policy<policies::digits2<N> > forwarding_policy;
- T v = detail::zeta_derivative_2<T>();
+ int n = N ? (std::min)(N, tools::digits<T>()) : tools::digits<T>();
+ T v = detail::zeta_derivative_2<T>(n);
v *= 6;
v /= boost::math::constants::pi<T, forwarding_policy>() * boost::math::constants::pi<T, forwarding_policy>();
v -= boost::math::constants::euler<T, forwarding_policy>();
Modified: sandbox/math_constants/libs/math/test/test_constants.cpp
==============================================================================
--- sandbox/math_constants/libs/math/test/test_constants.cpp (original)
+++ sandbox/math_constants/libs/math/test/test_constants.cpp 2012-01-08 13:22:24 EST (Sun, 08 Jan 2012)
@@ -56,6 +56,12 @@
big_real_concept(const T& t, typename enable_if<is_convertible<T, real_concept> >::type* = 0) : real_concept(t) {}
};
+inline int itrunc(const big_real_concept& val)
+{
+ BOOST_MATH_STD_USING
+ return itrunc(val.value());
+}
+
}
namespace tools{
@@ -94,30 +100,114 @@
//std::cout << "Precision for type " << typeid(RealType).name() << " is " << t1::value << "." << std::endl;
using namespace boost::math::constants;
- using namespace std; // Help ADL of std exp, log...
- using std::exp;
+ BOOST_MATH_STD_USING
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(3.14159265358979323846264338327950288419716939937510L), pi<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(3.14159265358979323846264338327950288419716939937510L), (pi<RealType, boost::math::policies::policy<> >)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(sqrt(3.14159265358979323846264338327950288419716939937510L/2)), root_half_pi<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(sqrt(3.14159265358979323846264338327950288419716939937510L * 2)), root_two_pi<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(sqrt(log(4.0L))), root_ln_four<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(2.71828182845904523536028747135266249775724709369995L), e<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(0.5), half<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(sqrt(2.0L)), root_two<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(log(2.0L)), ln_two<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(log(log(2.0L))), ln_ln_two<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(1)/3, third<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(2)/3, twothirds<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), root_half_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), root_two_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.5, half<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, euler<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), root_two<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log(2.0L), ln_two<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1)/3, third<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2)/3, twothirds<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, pi_minus_three<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, four_minus_pi<RealType>(), tolerance);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L)), pow23_four_minus_pi<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(exp(-0.5L)), exp_minus_half<RealType>(), tolerance);
-#else
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi<RealType>(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(exp(-0.5)), exp_minus_half<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), pow23_four_minus_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), pi_pow_e<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), cbrt_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), exp_minus_half<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), e_pow_pi<RealType>(), tolerance);
+
+
+#else // Only double, so no suffix L.
+ BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), pow23_four_minus_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), pi_pow_e<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), cbrt_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), exp_minus_half<RealType>(), tolerance);
#endif
- BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(0.57721566490153286060651209008240243104259335L), euler<RealType>(), tolerance);
+ // Rational fractions.
+ BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, third<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, two_thirds<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.75L, three_quarters<RealType>(), tolerance);
+ // Two and related.
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), root_two<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), root_three<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, half_root_two<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log(2.L), ln_two<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), one_div_root_two<RealType>(), tolerance);
+
+ // pi.
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, half_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, third_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, sixth_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, two_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, three_quarters_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, four_thirds_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), one_div_two_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), root_half_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), root_two_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), one_div_root_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), one_div_root_two_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L), root_one_div_pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L - 3.L, pi_minus_three<RealType>(), tolerance * 2 ); // tolerance * 2 because of cancellation loss.
+ BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, four_minus_pi<RealType>(), tolerance );
+ // BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), pow23_four_minus_pi<RealType>(), tolerance); See above.
+ //
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), pi_pow_e<RealType>(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, pi_sqr<RealType>(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L/6, pi_sqr_div_six<RealType>(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, pi_cubed<RealType>(), tolerance); // See above.
+
+ // BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, cbrt_pi<RealType>(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(cbrt_pi<RealType>() * cbrt_pi<RealType>() * cbrt_pi<RealType>(), pi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION((1)/cbrt_pi<RealType>(), one_div_cbrt_pi<RealType>(), tolerance);
+
+ // Euler
+ BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e<RealType>(), tolerance);
+
+ //BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), exp_minus_half<RealType>(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(pow(e<RealType>(), pi<RealType>()), e_pow_pi<RealType>(), tolerance); // See also above.
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(e<RealType>()), root_e<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log10(e<RealType>()), log10_e<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1/log10(e<RealType>()), one_div_log10_e<RealType>(), tolerance);
+
+ // Trigonmetric
+ BOOST_CHECK_CLOSE_FRACTION(pi<RealType>()/180, degree<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(180 / pi<RealType>(), radian<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sin(1.L), sin_one<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cos(1.L), cos_one<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sinh(1.L), sinh_one<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cosh(1.L), cosh_one<RealType>(), tolerance);
+
+ // Phi
+ BOOST_CHECK_CLOSE_FRACTION((1.L + sqrt(5.L)) /2, phi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log((1.L + sqrt(5.L)) /2), ln_phi<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1.L / log((1.L + sqrt(5.L)) /2), one_div_ln_phi<RealType>(), tolerance);
+
+ //Euler's Gamma
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104215933593992L, euler<RealType>(), tolerance); // (sequence A001620 in OEIS).
+ BOOST_CHECK_CLOSE_FRACTION(1.L/ 0.57721566490153286060651209008240243104215933593992L, one_div_euler<RealType>(), tolerance); // (from sequence A001620 in OEIS).
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104215933593992L * 0.57721566490153286060651209008240243104215933593992L, euler_sqr<RealType>(), tolerance); // (from sequence A001620 in OEIS).
+
+ // Misc
+ BOOST_CHECK_CLOSE_FRACTION(1.644934066848226436472415166646025189218949901206L, zeta_two<RealType>(), tolerance); // A013661 as a constant (usually base 10) in OEIS.
+ BOOST_CHECK_CLOSE_FRACTION(1.20205690315959428539973816151144999076498629234049888179227L, zeta_three<RealType>(), tolerance); // (sequence A002117 in OEIS)
+ BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213L, catalan<RealType>(), tolerance); // A006752 as a constant in OEIS.
+ BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, extreme_value_skewness<RealType>(), tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
+ BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, rayleigh_skewness<RealType>(), tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
+ BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess<RealType>(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, khinchin<RealType>(), tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
+ BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011L, glaisher<RealType>(), tolerance ); // https://oeis.org/A074962/constant
//
// Last of all come the test cases that behave differently if we're calculating the constants on the fly:
@@ -146,28 +236,112 @@
using namespace boost::math::float_constants;
BOOST_MATH_STD_USING
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510L), pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510L/2)), root_half_pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510L * 2)), root_two_pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(log(4.0L))), root_ln_four, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2.71828182845904523536028747135266249775724709369995L), e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F), pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F/2)), root_half_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F * 2)), root_two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(log(4.0F))), root_ln_four, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2.71828182845904523536028747135266249775724709369995F), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.5), half, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.57721566490153286060651209008240243104259335L), euler, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.0L)), root_two, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(2.0L)), ln_two, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(log(2.0L))), ln_ln_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.57721566490153286060651209008240243104259335F), euler, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.0F)), root_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(2.0F)), ln_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(log(2.0F))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1)/3, third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2)/3, twothirds, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.14159265358979323846264338327950288419716939937510F), pi_minus_three, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(4.F - 3.14159265358979323846264338327950288419716939937510F), four_minus_pi, tolerance);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L)), pow23_four_minus_pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(exp(-0.5L)), exp_minus_half, tolerance);
-#else
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((4 - 3.14159265358979323846264338327950288419716939937510F), 1.5F)), pow23_four_minus_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 2.71828182845904523536028747135266249775724709369995F)), pi_pow_e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 0.33333333333333333333333333333333333333333333333333F)), cbrt_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(exp(-0.5F)), exp_minus_half, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow(2.71828182845904523536028747135266249775724709369995F, 3.14159265358979323846264338327950288419716939937510F)), e_pow_pi, tolerance);
+
+
+#else // Only double, so no suffix F.
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(exp(-0.5)), exp_minus_half, tolerance);
#endif
+ // Rational fractions.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.333333333333333333333333333333333333333F), third, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.666666666666666666666666666666666666667F), two_thirds, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.75F), three_quarters, tolerance);
+ // Two and related.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.F)), root_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.F)), root_three, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.F)/2), half_root_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(2.F)), ln_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(log(2.0F))), ln_ln_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(log(4.0F))), root_ln_four, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1/sqrt(2.0F)), one_div_root_two, tolerance);
+
+ // pi.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F), pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/2), half_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/3), third_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/6), sixth_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2 * 3.14159265358979323846264338327950288419716939937510F), two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3 * 3.14159265358979323846264338327950288419716939937510F / 4), three_quarters_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(4 * 3.14159265358979323846264338327950288419716939937510F / 3), four_thirds_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1 / (2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F / 2)), root_half_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), root_two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1 / sqrt(3.14159265358979323846264338327950288419716939937510F)), one_div_root_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_root_two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(1. / 3.14159265358979323846264338327950288419716939937510F)), root_one_div_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510L - 3.L), pi_minus_three, tolerance * 2 ); // tolerance * 2 because of cancellation loss.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(4.L - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, tolerance );
+ // BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((4 - 3.14159265358979323846264338327950288419716939937510F), 1.5F)), pow23_four_minus_pi, tolerance); See above.
+ //
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 2.71828182845904523536028747135266249775724709369995F)), pi_pow_e, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), pi_sqr, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F/6), pi_sqr_div_six, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), pi_cubed, tolerance); // See above.
+
+ // BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), cbrt_pi, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION((static_cast<float>(1)/cbrt_pi), one_div_cbrt_pi, tolerance);
+
+ // Euler
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2.71828182845904523536028747135266249775724709369995F), e, tolerance);
+
+ //BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(exp(-0.5F)), exp_minus_half, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(pow(e, pi), e_pow_pi, tolerance); // See also above.
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(e), root_e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log10(e), log10_e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1)/log10(e), one_div_log10_e, tolerance);
+
+ // Trigonmetric
+ BOOST_CHECK_CLOSE_FRACTION(pi/180, degree, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(180 / pi, radian, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sin(1.F), sin_one, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cos(1.F), cos_one, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sinh(1.F), sinh_one, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cosh(1.F), cosh_one, tolerance);
+
+ // Phi
+ BOOST_CHECK_CLOSE_FRACTION((1.F + sqrt(5.F)) /2, phi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log((1.F + sqrt(5.F)) /2), ln_phi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1.F / log((1.F + sqrt(5.F)) /2), one_div_ln_phi, tolerance);
+
+ //Euler's Gamma
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104215933593992F, euler, tolerance); // (sequence A001620 in OEIS).
+ BOOST_CHECK_CLOSE_FRACTION(1.F/ 0.57721566490153286060651209008240243104215933593992F, one_div_euler, tolerance); // (from sequence A001620 in OEIS).
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104215933593992F * 0.57721566490153286060651209008240243104215933593992F, euler_sqr, tolerance); // (from sequence A001620 in OEIS).
+
+ // Misc
+ BOOST_CHECK_CLOSE_FRACTION(1.644934066848226436472415166646025189218949901206F, zeta_two, tolerance); // A013661 as a constant (usually base 10) in OEIS.
+ BOOST_CHECK_CLOSE_FRACTION(1.20205690315959428539973816151144999076498629234049888179227F, zeta_three, tolerance); // (sequence A002117 in OEIS)
+ BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213F, catalan, tolerance); // A006752 as a constant in OEIS.
+ BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150F, extreme_value_skewness, tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
+ BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067F, rayleigh_skewness, tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
+ BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01F, rayleigh_kurtosis_excess, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515F, khinchin, tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
+ BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011F, glaisher, tolerance ); // https://oeis.org/A074962/constant
} // template <class RealType>void test_spots(RealType)
@@ -182,28 +356,112 @@
using namespace boost::math::double_constants;
BOOST_MATH_STD_USING
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510L), pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510L/2)), root_half_pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510L * 2)), root_two_pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(log(4.0L))), root_ln_four, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2.71828182845904523536028747135266249775724709369995L), e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510), pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510/2)), root_half_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510 * 2)), root_two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(log(4.0))), root_ln_four, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2.71828182845904523536028747135266249775724709369995), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.5), half, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.57721566490153286060651209008240243104259335L), euler, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.0L)), root_two, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(2.0L)), ln_two, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(log(2.0L))), ln_ln_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.57721566490153286060651209008240243104259335), euler, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.0)), root_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(2.0)), ln_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(log(2.0))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1)/3, third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2)/3, twothirds, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.14159265358979323846264338327950288419716939937510), pi_minus_three, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(4. - 3.14159265358979323846264338327950288419716939937510), four_minus_pi, tolerance);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L)), pow23_four_minus_pi, tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(exp(-0.5L)), exp_minus_half, tolerance);
-#else
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(exp(-0.5)), exp_minus_half, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow(2.71828182845904523536028747135266249775724709369995, 3.14159265358979323846264338327950288419716939937510)), e_pow_pi, tolerance);
+
+
+#else // Only double, so no suffix .
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(exp(-0.5)), exp_minus_half, tolerance);
#endif
+ // Rational fractions.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.333333333333333333333333333333333333333), third, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.666666666666666666666666666666666666667), two_thirds, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.75), three_quarters, tolerance);
+ // Two and related.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.)), root_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.)), root_three, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.)/2), half_root_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(2.)), ln_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(log(2.0))), ln_ln_two, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(log(4.0))), root_ln_four, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1/sqrt(2.0)), one_div_root_two, tolerance);
+
+ // pi.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510), pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510/2), half_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510/3), third_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510/6), sixth_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2 * 3.14159265358979323846264338327950288419716939937510), two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3 * 3.14159265358979323846264338327950288419716939937510 / 4), three_quarters_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(4 * 3.14159265358979323846264338327950288419716939937510 / 3), four_thirds_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1 / (2 * 3.14159265358979323846264338327950288419716939937510)), one_div_two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510 / 2)), root_half_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), root_two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1 / sqrt(3.14159265358979323846264338327950288419716939937510)), one_div_root_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), one_div_root_two_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(1. / 3.14159265358979323846264338327950288419716939937510)), root_one_div_pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510 - 3.), pi_minus_three, tolerance * 2 ); // tolerance * 2 because of cancellation loss.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(4. - 3.14159265358979323846264338327950288419716939937510), four_minus_pi, tolerance );
+ // BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance); See above.
+ //
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), pi_sqr, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510/6), pi_sqr_div_six, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), pi_cubed, tolerance); // See above.
+
+ // BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), cbrt_pi, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION((static_cast<double>(1)/cbrt_pi), one_div_cbrt_pi, tolerance);
+
+ // Euler
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2.71828182845904523536028747135266249775724709369995), e, tolerance);
+
+ //BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(exp(-0.5)), exp_minus_half, tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(pow(e, pi), e_pow_pi, tolerance); // See also above.
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(e), root_e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log10(e), log10_e, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1)/log10(e), one_div_log10_e, tolerance);
+
+ // Trigonmetric
+ BOOST_CHECK_CLOSE_FRACTION(pi/180, degree, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(180 / pi, radian, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sin(1.), sin_one, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cos(1.), cos_one, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sinh(1.), sinh_one, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cosh(1.), cosh_one, tolerance);
+
+ // Phi
+ BOOST_CHECK_CLOSE_FRACTION((1. + sqrt(5.)) /2, phi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log((1. + sqrt(5.)) /2), ln_phi, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1. / log((1. + sqrt(5.)) /2), one_div_ln_phi, tolerance);
+
+ //Euler's Gamma
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104215933593992, euler, tolerance); // (sequence A001620 in OEIS).
+ BOOST_CHECK_CLOSE_FRACTION(1./ 0.57721566490153286060651209008240243104215933593992, one_div_euler, tolerance); // (from sequence A001620 in OEIS).
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104215933593992 * 0.57721566490153286060651209008240243104215933593992, euler_sqr, tolerance); // (from sequence A001620 in OEIS).
+
+ // Misc
+ BOOST_CHECK_CLOSE_FRACTION(1.644934066848226436472415166646025189218949901206, zeta_two, tolerance); // A013661 as a constant (usually base 10) in OEIS.
+ BOOST_CHECK_CLOSE_FRACTION(1.20205690315959428539973816151144999076498629234049888179227, zeta_three, tolerance); // (sequence A002117 in OEIS)
+ BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213, catalan, tolerance); // A006752 as a constant in OEIS.
+ BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150, extreme_value_skewness, tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
+ BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067, rayleigh_skewness, tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
+ BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01, rayleigh_kurtosis_excess, tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515, khinchin, tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
+ BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011, glaisher, tolerance ); // https://oeis.org/A074962/constant
} // template <class RealType>void test_spots(RealType)
@@ -325,7 +583,7 @@
BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213L, catalan, tolerance); // A006752 as a constant in OEIS.
BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, extreme_value_skewness, tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, rayleigh_skewness, tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
- BOOST_CHECK_CLOSE_FRACTION(-(6 * pi_sqr - 24 * pi + 16)/((four_minus_pi) * (four_minus_pi)), rayleigh_kurtosis_excess, tolerance * 20); // Cancellation loss of accuracy.
+ BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess, tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, khinchin, tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011L, glaisher, tolerance ); // https://oeis.org/A074962/constant
@@ -337,39 +595,139 @@
// Basic sanity checks for constants using real_concept.
// Parameter Policy is used to control precision.
- boost::math::concepts::real_concept tolerance = boost::math::tools::epsilon<boost::math::concepts::real_concept>() * 2; // double
- std::cout << "Tolerance for type " << typeid(boost::math::concepts::real_concept).name() << " is " << tolerance << "." << std::endl;
+ using boost::math::concepts::real_concept;
+
+ boost::math::concepts::real_concept tolerance = boost::math::tools::epsilon<real_concept>() * 2; // double
+ std::cout << "Tolerance for type " << typeid(real_concept).name() << " is " << tolerance << "." << std::endl;
//typedef typename boost::math::policies::precision<boost::math::concepts::real_concept, boost::math::policies::policy<> >::type t1;
// A precision of zero means we don't know what the precision of this type is until runtime.
//std::cout << "Precision for type " << typeid(boost::math::concepts::real_concept).name() << " is " << t1::value << "." << std::endl;
using namespace boost::math::constants;
- using namespace std; // Help ADL of std exp, log...
- using std::exp;
+ BOOST_MATH_STD_USING
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(3.14159265358979323846264338327950288419716939937510L), (pi<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(sqrt(3.14159265358979323846264338327950288419716939937510L)), (root_pi<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(sqrt(3.14159265358979323846264338327950288419716939937510L/2)), (root_half_pi<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(sqrt(3.14159265358979323846264338327950288419716939937510L * 2)), (root_two_pi<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(sqrt(log(4.0L))), (root_ln_four<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(2.71828182845904523536028747135266249775724709369995L), (e<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(0.5), (half<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(0.57721566490153286060651209008240243104259335L), (euler<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(sqrt(2.0L)), (root_two<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(log(2.0L)), (ln_two<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(log(log(2.0L))), (ln_ln_two<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(1)/3, (third<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(2)/3, (twothirds<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(0.14159265358979323846264338327950288419716939937510L), (pi_minus_three<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(4. - 3.14159265358979323846264338327950288419716939937510L), (four_minus_pi<boost::math::concepts::real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), (root_half_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), (root_two_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.5, (half<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, (euler<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), (root_two<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log(2.0L), (ln_two<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1)/3, (third<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2)/3, (twothirds<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, (pi_minus_three<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, (four_minus_pi<real_concept, Policy>)(), tolerance);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L)), (pow23_four_minus_pi<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(exp(-0.5L)), (exp_minus_half<boost::math::concepts::real_concept, Policy>)(), tolerance);
-#else
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), (pow23_four_minus_pi<boost::math::concepts::real_concept, Policy>)(), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(exp(-0.5)), (exp_minus_half<boost::math::concepts::real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), (pow23_four_minus_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), (pi_pow_e<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), (cbrt_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), (exp_minus_half<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), (e_pow_pi<real_concept, Policy>)(), tolerance);
+
+
+#else // Only double, so no suffix L.
+ BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), (pow23_four_minus_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), (pi_pow_e<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), (cbrt_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), (exp_minus_half<real_concept, Policy>)(), tolerance);
#endif
+ // Rational fractions.
+ BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, (third<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, (two_thirds<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(0.75L, (three_quarters<real_concept, Policy>)(), tolerance);
+ // Two and related.
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), (root_two<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), (root_three<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, (half_root_two<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log(2.L), (ln_two<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), (one_div_root_two<real_concept, Policy>)(), tolerance);
+
+ // pi.
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, (half_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, (third_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, (sixth_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, (two_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, (three_quarters_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, (four_thirds_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_two_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), (root_half_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (root_two_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), (one_div_root_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_root_two_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L), (root_one_div_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L - 3.L, (pi_minus_three<real_concept, Policy>)(), tolerance * 2 ); // tolerance * 2 because of cancellation loss.
+ BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, (four_minus_pi<real_concept, Policy>)(), tolerance );
+ // BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), (pow23_four_minus_pi<real_concept, Policy>)(), tolerance); See above.
+ //
+ BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), (pi_pow_e<real_concept, Policy>)(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (pi_sqr<real_concept, Policy>)(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L/6, (pi_sqr_div_six<real_concept, Policy>)(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (pi_cubed<real_concept, Policy>)(), tolerance); // See above.
+
+ // BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (cbrt_pi<real_concept, Policy>)(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION((cbrt_pi<real_concept, Policy>)() * (cbrt_pi<real_concept, Policy>)() * (cbrt_pi<real_concept, Policy>)(), (pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION((1)/(cbrt_pi<real_concept, Policy>)(), (one_div_cbrt_pi<real_concept, Policy>)(), tolerance);
+
+ // Euler
+ BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e<real_concept, Policy>)(), tolerance);
+
+ //BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), (exp_minus_half<real_concept, Policy>)(), tolerance); // See above.
+ BOOST_CHECK_CLOSE_FRACTION(pow(e<real_concept, Policy>(), (pi<real_concept, Policy>)()), (e_pow_pi<real_concept, Policy>)(), tolerance); // See also above.
+ BOOST_CHECK_CLOSE_FRACTION(sqrt(e<real_concept, Policy>()), (root_e<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log10(e<real_concept, Policy>()), (log10_e<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1/log10(e<real_concept, Policy>()), (one_div_log10_e<real_concept, Policy>)(), tolerance);
+
+ // Trigonmetric
+ BOOST_CHECK_CLOSE_FRACTION((pi<real_concept, Policy>)()/180, (degree<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(180 / (pi<real_concept, Policy>)(), (radian<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sin(1.L), (sin_one<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cos(1.L), (cos_one<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(sinh(1.L), (sinh_one<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cosh(1.L), (cosh_one<real_concept, Policy>)(), tolerance);
+
+ // Phi
+ BOOST_CHECK_CLOSE_FRACTION((1.L + sqrt(5.L)) /2, (phi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(log((1.L + sqrt(5.L)) /2), (ln_phi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(1.L / log((1.L + sqrt(5.L)) /2), (one_div_ln_phi<real_concept, Policy>)(), tolerance);
+
+ //Euler's Gamma
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104215933593992L, (euler<real_concept, Policy>)(), tolerance); // (sequence A001620 in OEIS).
+ BOOST_CHECK_CLOSE_FRACTION(1.L/ 0.57721566490153286060651209008240243104215933593992L, (one_div_euler<real_concept, Policy>)(), tolerance); // (from sequence A001620 in OEIS).
+ BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104215933593992L * 0.57721566490153286060651209008240243104215933593992L, (euler_sqr<real_concept, Policy>)(), tolerance); // (from sequence A001620 in OEIS).
+
+ // Misc
+ BOOST_CHECK_CLOSE_FRACTION(1.644934066848226436472415166646025189218949901206L, (zeta_two<real_concept, Policy>)(), tolerance); // A013661 as a constant (usually base 10) in OEIS.
+ BOOST_CHECK_CLOSE_FRACTION(1.20205690315959428539973816151144999076498629234049888179227L, (zeta_three<real_concept, Policy>)(), tolerance); // (sequence A002117 in OEIS)
+ BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213L, (catalan<real_concept, Policy>)(), tolerance); // A006752 as a constant in OEIS.
+ BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, (extreme_value_skewness<real_concept, Policy>)(), tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
+ BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, (rayleigh_skewness<real_concept, Policy>)(), tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
+ BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, (rayleigh_kurtosis_excess<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, (khinchin<real_concept, Policy>)(), tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
+ BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011L, (glaisher<real_concept, Policy>)(), tolerance ); // https://oeis.org/A074962/constant
+
+ //
+ // Last of all come the test cases that behave differently if we're calculating the constants on the fly:
+ //
+ if(boost::math::tools::digits<real_concept>() > boost::math::constants::max_string_digits)
+ {
+ // This suffers from cancellation error, so increased tolerance:
+ BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi<real_concept, Policy>)(), tolerance * 3);
+ BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three<real_concept, Policy>)(), tolerance * 3);
+ }
+ else
+ {
+ BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi<real_concept, Policy>)(), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three<real_concept, Policy>)(), tolerance);
+ }
} // template <class boost::math::concepts::real_concept>void test_spots(boost::math::concepts::real_concept)
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