713 lines
28 KiB
Plaintext
713 lines
28 KiB
Plaintext
///////////////////////////////////////////////////////////////////////////////
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// Copyright 2013 John Maddock
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// Distributed under the Boost
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// Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_BERNOULLI_DETAIL_HPP
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#define BOOST_MATH_BERNOULLI_DETAIL_HPP
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#include <boost/config.hpp>
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#include <boost/detail/lightweight_mutex.hpp>
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#include <boost/utility/enable_if.hpp>
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#include <boost/math/tools/toms748_solve.hpp>
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#include <vector>
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#ifdef BOOST_HAS_THREADS
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#ifndef BOOST_NO_CXX11_HDR_ATOMIC
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# include <atomic>
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# define BOOST_MATH_ATOMIC_NS std
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#if ATOMIC_INT_LOCK_FREE == 2
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typedef std::atomic<int> atomic_counter_type;
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typedef int atomic_integer_type;
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#elif ATOMIC_SHORT_LOCK_FREE == 2
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typedef std::atomic<short> atomic_counter_type;
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typedef short atomic_integer_type;
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#elif ATOMIC_LONG_LOCK_FREE == 2
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typedef std::atomic<long> atomic_counter_type;
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typedef long atomic_integer_type;
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#elif ATOMIC_LLONG_LOCK_FREE == 2
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typedef std::atomic<long long> atomic_counter_type;
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typedef long long atomic_integer_type;
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#else
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# define BOOST_MATH_NO_ATOMIC_INT
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#endif
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#else // BOOST_NO_CXX11_HDR_ATOMIC
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//
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// We need Boost.Atomic, but on any platform that supports auto-linking we do
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// not need to link against a separate library:
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//
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#define BOOST_ATOMIC_NO_LIB
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#include <boost/atomic.hpp>
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# define BOOST_MATH_ATOMIC_NS boost
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namespace boost{ namespace math{ namespace detail{
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//
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// We need a type to use as an atomic counter:
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//
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#if BOOST_ATOMIC_INT_LOCK_FREE == 2
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typedef boost::atomic<int> atomic_counter_type;
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typedef int atomic_integer_type;
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#elif BOOST_ATOMIC_SHORT_LOCK_FREE == 2
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typedef boost::atomic<short> atomic_counter_type;
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typedef short atomic_integer_type;
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#elif BOOST_ATOMIC_LONG_LOCK_FREE == 2
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typedef boost::atomic<long> atomic_counter_type;
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typedef long atomic_integer_type;
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#elif BOOST_ATOMIC_LLONG_LOCK_FREE == 2
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typedef boost::atomic<long long> atomic_counter_type;
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typedef long long atomic_integer_type;
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#else
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# define BOOST_MATH_NO_ATOMIC_INT
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#endif
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}}} // namespaces
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#endif // BOOST_NO_CXX11_HDR_ATOMIC
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#endif // BOOST_HAS_THREADS
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namespace boost{ namespace math{ namespace detail{
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//
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// Asymptotic expansion for B2n due to
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// Luschny LogB3 formula (http://www.luschny.de/math/primes/bernincl.html)
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//
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template <class T, class Policy>
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T b2n_asymptotic(int n)
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{
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BOOST_MATH_STD_USING
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const T nx = static_cast<T>(n);
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const T nx2(nx * nx);
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const T approximate_log_of_bernoulli_bn =
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((boost::math::constants::half<T>() + nx) * log(nx))
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+ ((boost::math::constants::half<T>() - nx) * log(boost::math::constants::pi<T>()))
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+ (((T(3) / 2) - nx) * boost::math::constants::ln_two<T>())
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+ ((nx * (T(2) - (nx2 * 7) * (1 + ((nx2 * 30) * ((nx2 * 12) - 1))))) / (((nx2 * nx2) * nx2) * 2520));
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return ((n / 2) & 1 ? 1 : -1) * (approximate_log_of_bernoulli_bn > tools::log_max_value<T>()
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? policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, nx, Policy())
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: static_cast<T>(exp(approximate_log_of_bernoulli_bn)));
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}
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template <class T, class Policy>
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T t2n_asymptotic(int n)
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{
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BOOST_MATH_STD_USING
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// Just get B2n and convert to a Tangent number:
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T t2n = fabs(b2n_asymptotic<T, Policy>(2 * n)) / (2 * n);
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T p2 = ldexp(T(1), n);
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if(tools::max_value<T>() / p2 < t2n)
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return policies::raise_overflow_error<T>("boost::math::tangent_t2n<%1%>(std::size_t)", 0, T(n), Policy());
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t2n *= p2;
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p2 -= 1;
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if(tools::max_value<T>() / p2 < t2n)
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return policies::raise_overflow_error<T>("boost::math::tangent_t2n<%1%>(std::size_t)", 0, Policy());
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t2n *= p2;
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return t2n;
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}
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//
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// We need to know the approximate value of /n/ which will
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// cause bernoulli_b2n<T>(n) to return infinity - this allows
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// us to elude a great deal of runtime checking for values below
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// n, and only perform the full overflow checks when we know that we're
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// getting close to the point where our calculations will overflow.
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// We use Luschny's LogB3 formula (http://www.luschny.de/math/primes/bernincl.html)
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// to find the limit, and since we're dealing with the log of the Bernoulli numbers
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// we need only perform the calculation at double precision and not with T
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// (which may be a multiprecision type). The limit returned is within 1 of the true
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// limit for all the types tested. Note that although the code below is basically
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// the same as b2n_asymptotic above, it has been recast as a continuous real-valued
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// function as this makes the root finding go smoother/faster. It also omits the
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// sign of the Bernoulli number.
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//
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struct max_bernoulli_root_functor
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{
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max_bernoulli_root_functor(long long t) : target(static_cast<double>(t)) {}
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double operator()(double n)
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{
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BOOST_MATH_STD_USING
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// Luschny LogB3(n) formula.
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const double nx2(n * n);
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const double approximate_log_of_bernoulli_bn
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= ((boost::math::constants::half<double>() + n) * log(n))
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+ ((boost::math::constants::half<double>() - n) * log(boost::math::constants::pi<double>()))
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+ (((double(3) / 2) - n) * boost::math::constants::ln_two<double>())
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+ ((n * (2 - (nx2 * 7) * (1 + ((nx2 * 30) * ((nx2 * 12) - 1))))) / (((nx2 * nx2) * nx2) * 2520));
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return approximate_log_of_bernoulli_bn - target;
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}
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private:
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double target;
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};
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template <class T, class Policy>
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inline std::size_t find_bernoulli_overflow_limit(const mpl::false_&)
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{
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long long t = lltrunc(boost::math::tools::log_max_value<T>());
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max_bernoulli_root_functor fun(t);
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boost::math::tools::equal_floor tol;
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boost::uintmax_t max_iter = boost::math::policies::get_max_root_iterations<Policy>();
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return static_cast<std::size_t>(boost::math::tools::toms748_solve(fun, sqrt(double(t)), double(t), tol, max_iter).first) / 2;
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}
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template <class T, class Policy>
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inline std::size_t find_bernoulli_overflow_limit(const mpl::true_&)
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{
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return max_bernoulli_index<bernoulli_imp_variant<T>::value>::value;
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}
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template <class T, class Policy>
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std::size_t b2n_overflow_limit()
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{
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// This routine is called at program startup if it's called at all:
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// that guarantees safe initialization of the static variable.
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typedef mpl::bool_<(bernoulli_imp_variant<T>::value >= 1) && (bernoulli_imp_variant<T>::value <= 3)> tag_type;
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static const std::size_t lim = find_bernoulli_overflow_limit<T, Policy>(tag_type());
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return lim;
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}
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//
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// The tangent numbers grow larger much more rapidly than the Bernoulli numbers do....
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// so to compute the Bernoulli numbers from the tangent numbers, we need to avoid spurious
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// overflow in the calculation, we can do this by scaling all the tangent number by some scale factor:
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//
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template <class T>
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inline typename enable_if_c<std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::radix == 2), T>::type tangent_scale_factor()
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{
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BOOST_MATH_STD_USING
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return ldexp(T(1), std::numeric_limits<T>::min_exponent + 5);
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}
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template <class T>
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inline typename disable_if_c<std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::radix == 2), T>::type tangent_scale_factor()
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{
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return tools::min_value<T>() * 16;
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}
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//
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// Initializer: ensure all our constants are initialized prior to the first call of main:
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//
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template <class T, class Policy>
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struct bernoulli_initializer
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{
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struct init
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{
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init()
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{
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//
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// We call twice, once to initialize our static table, and once to
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// initialize our dymanic table:
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//
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boost::math::bernoulli_b2n<T>(2, Policy());
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#ifndef BOOST_NO_EXCEPTIONS
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try{
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#endif
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boost::math::bernoulli_b2n<T>(max_bernoulli_b2n<T>::value + 1, Policy());
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#ifndef BOOST_NO_EXCEPTIONS
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} catch(const std::overflow_error&){}
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#endif
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boost::math::tangent_t2n<T>(2, Policy());
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}
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void force_instantiate()const{}
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};
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static const init initializer;
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static void force_instantiate()
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{
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initializer.force_instantiate();
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}
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};
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template <class T, class Policy>
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const typename bernoulli_initializer<T, Policy>::init bernoulli_initializer<T, Policy>::initializer;
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//
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// We need something to act as a cache for our calculated Bernoulli numbers. In order to
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// ensure both fast access and thread safety, we need a stable table which may be extended
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// in size, but which never reallocates: that way values already calculated may be accessed
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// concurrently with another thread extending the table with new values.
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//
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// Very very simple vector class that will never allocate more than once, we could use
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// boost::container::static_vector here, but that allocates on the stack, which may well
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// cause issues for the amount of memory we want in the extreme case...
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//
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template <class T>
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struct fixed_vector : private std::allocator<T>
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{
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typedef unsigned size_type;
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typedef T* iterator;
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typedef const T* const_iterator;
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fixed_vector() : m_used(0)
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{
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std::size_t overflow_limit = 5 + b2n_overflow_limit<T, policies::policy<> >();
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m_capacity = static_cast<unsigned>((std::min)(overflow_limit, static_cast<std::size_t>(100000u)));
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m_data = this->allocate(m_capacity);
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}
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~fixed_vector()
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{
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for(unsigned i = 0; i < m_used; ++i)
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this->destroy(&m_data[i]);
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this->deallocate(m_data, m_capacity);
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}
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T& operator[](unsigned n) { BOOST_ASSERT(n < m_used); return m_data[n]; }
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const T& operator[](unsigned n)const { BOOST_ASSERT(n < m_used); return m_data[n]; }
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unsigned size()const { return m_used; }
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unsigned size() { return m_used; }
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void resize(unsigned n, const T& val)
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{
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if(n > m_capacity)
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{
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BOOST_THROW_EXCEPTION(std::runtime_error("Exhausted storage for Bernoulli numbers."));
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}
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for(unsigned i = m_used; i < n; ++i)
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new (m_data + i) T(val);
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m_used = n;
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}
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void resize(unsigned n) { resize(n, T()); }
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T* begin() { return m_data; }
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T* end() { return m_data + m_used; }
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T* begin()const { return m_data; }
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T* end()const { return m_data + m_used; }
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unsigned capacity()const { return m_capacity; }
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void clear() { m_used = 0; }
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private:
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T* m_data;
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unsigned m_used, m_capacity;
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};
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template <class T, class Policy>
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class bernoulli_numbers_cache
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{
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public:
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bernoulli_numbers_cache() : m_overflow_limit((std::numeric_limits<std::size_t>::max)())
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#if defined(BOOST_HAS_THREADS) && !defined(BOOST_MATH_NO_ATOMIC_INT)
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, m_counter(0)
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#endif
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, m_current_precision(boost::math::tools::digits<T>())
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{}
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typedef fixed_vector<T> container_type;
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void tangent(std::size_t m)
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{
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static const std::size_t min_overflow_index = b2n_overflow_limit<T, Policy>() - 1;
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tn.resize(static_cast<typename container_type::size_type>(m), T(0U));
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BOOST_MATH_INSTRUMENT_VARIABLE(min_overflow_index);
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std::size_t prev_size = m_intermediates.size();
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m_intermediates.resize(m, T(0U));
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if(prev_size == 0)
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{
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m_intermediates[1] = tangent_scale_factor<T>() /*T(1U)*/;
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tn[0U] = T(0U);
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tn[1U] = tangent_scale_factor<T>()/* T(1U)*/;
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BOOST_MATH_INSTRUMENT_VARIABLE(tn[0]);
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BOOST_MATH_INSTRUMENT_VARIABLE(tn[1]);
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}
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for(std::size_t i = std::max<size_t>(2, prev_size); i < m; i++)
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{
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bool overflow_check = false;
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if(i >= min_overflow_index && (boost::math::tools::max_value<T>() / (i-1) < m_intermediates[1]) )
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{
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std::fill(tn.begin() + i, tn.end(), boost::math::tools::max_value<T>());
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break;
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}
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m_intermediates[1] = m_intermediates[1] * (i-1);
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for(std::size_t j = 2; j <= i; j++)
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{
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overflow_check =
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(i >= min_overflow_index) && (
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(boost::math::tools::max_value<T>() / (i - j) < m_intermediates[j])
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|| (boost::math::tools::max_value<T>() / (i - j + 2) < m_intermediates[j-1])
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|| (boost::math::tools::max_value<T>() - m_intermediates[j] * (i - j) < m_intermediates[j-1] * (i - j + 2))
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|| ((boost::math::isinf)(m_intermediates[j]))
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);
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if(overflow_check)
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{
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std::fill(tn.begin() + i, tn.end(), boost::math::tools::max_value<T>());
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break;
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}
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m_intermediates[j] = m_intermediates[j] * (i - j) + m_intermediates[j-1] * (i - j + 2);
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}
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if(overflow_check)
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break; // already filled the tn...
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tn[static_cast<typename container_type::size_type>(i)] = m_intermediates[i];
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BOOST_MATH_INSTRUMENT_VARIABLE(i);
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BOOST_MATH_INSTRUMENT_VARIABLE(tn[static_cast<typename container_type::size_type>(i)]);
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}
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}
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void tangent_numbers_series(const std::size_t m)
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{
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BOOST_MATH_STD_USING
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static const std::size_t min_overflow_index = b2n_overflow_limit<T, Policy>() - 1;
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typename container_type::size_type old_size = bn.size();
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tangent(m);
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bn.resize(static_cast<typename container_type::size_type>(m));
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if(!old_size)
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{
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bn[0] = 1;
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old_size = 1;
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}
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T power_two(ldexp(T(1), static_cast<int>(2 * old_size)));
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for(std::size_t i = old_size; i < m; i++)
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{
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T b(static_cast<T>(i * 2));
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//
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// Not only do we need to take care to avoid spurious over/under flow in
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// the calculation, but we also need to avoid overflow altogether in case
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// we're calculating with a type where "bad things" happen in that case:
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//
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b = b / (power_two * tangent_scale_factor<T>());
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b /= (power_two - 1);
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bool overflow_check = (i >= min_overflow_index) && (tools::max_value<T>() / tn[static_cast<typename container_type::size_type>(i)] < b);
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if(overflow_check)
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{
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m_overflow_limit = i;
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while(i < m)
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{
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b = std::numeric_limits<T>::has_infinity ? std::numeric_limits<T>::infinity() : tools::max_value<T>();
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bn[static_cast<typename container_type::size_type>(i)] = ((i % 2U) ? b : T(-b));
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++i;
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}
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break;
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}
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else
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{
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b *= tn[static_cast<typename container_type::size_type>(i)];
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}
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power_two = ldexp(power_two, 2);
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const bool b_neg = i % 2 == 0;
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bn[static_cast<typename container_type::size_type>(i)] = ((!b_neg) ? b : T(-b));
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}
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}
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template <class OutputIterator>
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OutputIterator copy_bernoulli_numbers(OutputIterator out, std::size_t start, std::size_t n, const Policy& pol)
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{
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//
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// There are basically 3 thread safety options:
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//
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// 1) There are no threads (BOOST_HAS_THREADS is not defined).
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// 2) There are threads, but we do not have a true atomic integer type,
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// in this case we just use a mutex to guard against race conditions.
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// 3) There are threads, and we have an atomic integer: in this case we can
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// use the double-checked locking pattern to avoid thread synchronisation
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// when accessing values already in the cache.
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//
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// First off handle the common case for overflow and/or asymptotic expansion:
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//
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if(start + n > bn.capacity())
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{
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if(start < bn.capacity())
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{
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out = copy_bernoulli_numbers(out, start, bn.capacity() - start, pol);
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n -= bn.capacity() - start;
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start = static_cast<std::size_t>(bn.capacity());
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}
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if(start < b2n_overflow_limit<T, Policy>() + 2u)
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{
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for(; n; ++start, --n)
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{
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*out = b2n_asymptotic<T, Policy>(static_cast<typename container_type::size_type>(start * 2U));
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++out;
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}
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}
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for(; n; ++start, --n)
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{
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*out = policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(start), pol);
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++out;
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}
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return out;
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}
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#if !defined(BOOST_HAS_THREADS)
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//
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|
// Single threaded code, very simple:
|
|
//
|
|
if(m_current_precision < boost::math::tools::digits<T>())
|
|
{
|
|
bn.clear();
|
|
tn.clear();
|
|
m_intermediates.clear();
|
|
m_current_precision = boost::math::tools::digits<T>();
|
|
}
|
|
if(start + n >= bn.size())
|
|
{
|
|
std::size_t new_size = (std::min)((std::max)((std::max)(std::size_t(start + n), std::size_t(bn.size() + 20)), std::size_t(50)), std::size_t(bn.capacity()));
|
|
tangent_numbers_series(new_size);
|
|
}
|
|
|
|
for(std::size_t i = (std::max)(std::size_t(max_bernoulli_b2n<T>::value + 1), start); i < start + n; ++i)
|
|
{
|
|
*out = (i >= m_overflow_limit) ? policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(i), pol) : bn[i];
|
|
++out;
|
|
}
|
|
#elif defined(BOOST_MATH_NO_ATOMIC_INT)
|
|
//
|
|
// We need to grab a mutex every time we get here, for both readers and writers:
|
|
//
|
|
boost::detail::lightweight_mutex::scoped_lock l(m_mutex);
|
|
if(m_current_precision < boost::math::tools::digits<T>())
|
|
{
|
|
bn.clear();
|
|
tn.clear();
|
|
m_intermediates.clear();
|
|
m_current_precision = boost::math::tools::digits<T>();
|
|
}
|
|
if(start + n >= bn.size())
|
|
{
|
|
std::size_t new_size = (std::min)((std::max)((std::max)(std::size_t(start + n), std::size_t(bn.size() + 20)), std::size_t(50)), std::size_t(bn.capacity()));
|
|
tangent_numbers_series(new_size);
|
|
}
|
|
|
|
for(std::size_t i = (std::max)(std::size_t(max_bernoulli_b2n<T>::value + 1), start); i < start + n; ++i)
|
|
{
|
|
*out = (i >= m_overflow_limit) ? policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(i), pol) : bn[i];
|
|
++out;
|
|
}
|
|
|
|
#else
|
|
//
|
|
// Double-checked locking pattern, lets us access cached already cached values
|
|
// without locking:
|
|
//
|
|
// Get the counter and see if we need to calculate more constants:
|
|
//
|
|
if((static_cast<std::size_t>(m_counter.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < start + n)
|
|
|| (static_cast<int>(m_current_precision.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < boost::math::tools::digits<T>()))
|
|
{
|
|
boost::detail::lightweight_mutex::scoped_lock l(m_mutex);
|
|
|
|
if((static_cast<std::size_t>(m_counter.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < start + n)
|
|
|| (static_cast<int>(m_current_precision.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < boost::math::tools::digits<T>()))
|
|
{
|
|
if(static_cast<int>(m_current_precision.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < boost::math::tools::digits<T>())
|
|
{
|
|
bn.clear();
|
|
tn.clear();
|
|
m_intermediates.clear();
|
|
m_counter.store(0, BOOST_MATH_ATOMIC_NS::memory_order_release);
|
|
m_current_precision = boost::math::tools::digits<T>();
|
|
}
|
|
if(start + n >= bn.size())
|
|
{
|
|
std::size_t new_size = (std::min)((std::max)((std::max)(std::size_t(start + n), std::size_t(bn.size() + 20)), std::size_t(50)), std::size_t(bn.capacity()));
|
|
tangent_numbers_series(new_size);
|
|
}
|
|
m_counter.store(static_cast<atomic_integer_type>(bn.size()), BOOST_MATH_ATOMIC_NS::memory_order_release);
|
|
}
|
|
}
|
|
|
|
for(std::size_t i = (std::max)(static_cast<std::size_t>(max_bernoulli_b2n<T>::value + 1), start); i < start + n; ++i)
|
|
{
|
|
*out = (i >= m_overflow_limit) ? policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(i), pol) : bn[static_cast<typename container_type::size_type>(i)];
|
|
++out;
|
|
}
|
|
|
|
#endif
|
|
return out;
|
|
}
|
|
|
|
template <class OutputIterator>
|
|
OutputIterator copy_tangent_numbers(OutputIterator out, std::size_t start, std::size_t n, const Policy& pol)
|
|
{
|
|
//
|
|
// There are basically 3 thread safety options:
|
|
//
|
|
// 1) There are no threads (BOOST_HAS_THREADS is not defined).
|
|
// 2) There are threads, but we do not have a true atomic integer type,
|
|
// in this case we just use a mutex to guard against race conditions.
|
|
// 3) There are threads, and we have an atomic integer: in this case we can
|
|
// use the double-checked locking pattern to avoid thread synchronisation
|
|
// when accessing values already in the cache.
|
|
//
|
|
//
|
|
// First off handle the common case for overflow and/or asymptotic expansion:
|
|
//
|
|
if(start + n > bn.capacity())
|
|
{
|
|
if(start < bn.capacity())
|
|
{
|
|
out = copy_tangent_numbers(out, start, bn.capacity() - start, pol);
|
|
n -= bn.capacity() - start;
|
|
start = static_cast<std::size_t>(bn.capacity());
|
|
}
|
|
if(start < b2n_overflow_limit<T, Policy>() + 2u)
|
|
{
|
|
for(; n; ++start, --n)
|
|
{
|
|
*out = t2n_asymptotic<T, Policy>(static_cast<typename container_type::size_type>(start));
|
|
++out;
|
|
}
|
|
}
|
|
for(; n; ++start, --n)
|
|
{
|
|
*out = policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(start), pol);
|
|
++out;
|
|
}
|
|
return out;
|
|
}
|
|
#if !defined(BOOST_HAS_THREADS)
|
|
//
|
|
// Single threaded code, very simple:
|
|
//
|
|
if(m_current_precision < boost::math::tools::digits<T>())
|
|
{
|
|
bn.clear();
|
|
tn.clear();
|
|
m_intermediates.clear();
|
|
m_current_precision = boost::math::tools::digits<T>();
|
|
}
|
|
if(start + n >= bn.size())
|
|
{
|
|
std::size_t new_size = (std::min)((std::max)((std::max)(start + n, std::size_t(bn.size() + 20)), std::size_t(50)), std::size_t(bn.capacity()));
|
|
tangent_numbers_series(new_size);
|
|
}
|
|
|
|
for(std::size_t i = start; i < start + n; ++i)
|
|
{
|
|
if(i >= m_overflow_limit)
|
|
*out = policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(i), pol);
|
|
else
|
|
{
|
|
if(tools::max_value<T>() * tangent_scale_factor<T>() < tn[static_cast<typename container_type::size_type>(i)])
|
|
*out = policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(i), pol);
|
|
else
|
|
*out = tn[static_cast<typename container_type::size_type>(i)] / tangent_scale_factor<T>();
|
|
}
|
|
++out;
|
|
}
|
|
#elif defined(BOOST_MATH_NO_ATOMIC_INT)
|
|
//
|
|
// We need to grab a mutex every time we get here, for both readers and writers:
|
|
//
|
|
boost::detail::lightweight_mutex::scoped_lock l(m_mutex);
|
|
if(m_current_precision < boost::math::tools::digits<T>())
|
|
{
|
|
bn.clear();
|
|
tn.clear();
|
|
m_intermediates.clear();
|
|
m_current_precision = boost::math::tools::digits<T>();
|
|
}
|
|
if(start + n >= bn.size())
|
|
{
|
|
std::size_t new_size = (std::min)((std::max)((std::max)(start + n, std::size_t(bn.size() + 20)), std::size_t(50)), std::size_t(bn.capacity()));
|
|
tangent_numbers_series(new_size);
|
|
}
|
|
|
|
for(std::size_t i = start; i < start + n; ++i)
|
|
{
|
|
if(i >= m_overflow_limit)
|
|
*out = policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(i), pol);
|
|
else
|
|
{
|
|
if(tools::max_value<T>() * tangent_scale_factor<T>() < tn[static_cast<typename container_type::size_type>(i)])
|
|
*out = policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(i), pol);
|
|
else
|
|
*out = tn[static_cast<typename container_type::size_type>(i)] / tangent_scale_factor<T>();
|
|
}
|
|
++out;
|
|
}
|
|
|
|
#else
|
|
//
|
|
// Double-checked locking pattern, lets us access cached already cached values
|
|
// without locking:
|
|
//
|
|
// Get the counter and see if we need to calculate more constants:
|
|
//
|
|
if((static_cast<std::size_t>(m_counter.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < start + n)
|
|
|| (static_cast<int>(m_current_precision.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < boost::math::tools::digits<T>()))
|
|
{
|
|
boost::detail::lightweight_mutex::scoped_lock l(m_mutex);
|
|
|
|
if((static_cast<std::size_t>(m_counter.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < start + n)
|
|
|| (static_cast<int>(m_current_precision.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < boost::math::tools::digits<T>()))
|
|
{
|
|
if(static_cast<int>(m_current_precision.load(BOOST_MATH_ATOMIC_NS::memory_order_consume)) < boost::math::tools::digits<T>())
|
|
{
|
|
bn.clear();
|
|
tn.clear();
|
|
m_intermediates.clear();
|
|
m_counter.store(0, BOOST_MATH_ATOMIC_NS::memory_order_release);
|
|
m_current_precision = boost::math::tools::digits<T>();
|
|
}
|
|
if(start + n >= bn.size())
|
|
{
|
|
std::size_t new_size = (std::min)((std::max)((std::max)(start + n, std::size_t(bn.size() + 20)), std::size_t(50)), std::size_t(bn.capacity()));
|
|
tangent_numbers_series(new_size);
|
|
}
|
|
m_counter.store(static_cast<atomic_integer_type>(bn.size()), BOOST_MATH_ATOMIC_NS::memory_order_release);
|
|
}
|
|
}
|
|
|
|
for(std::size_t i = start; i < start + n; ++i)
|
|
{
|
|
if(i >= m_overflow_limit)
|
|
*out = policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(i), pol);
|
|
else
|
|
{
|
|
if(tools::max_value<T>() * tangent_scale_factor<T>() < tn[static_cast<typename container_type::size_type>(i)])
|
|
*out = policies::raise_overflow_error<T>("boost::math::bernoulli_b2n<%1%>(std::size_t)", 0, T(i), pol);
|
|
else
|
|
*out = tn[static_cast<typename container_type::size_type>(i)] / tangent_scale_factor<T>();
|
|
}
|
|
++out;
|
|
}
|
|
|
|
#endif
|
|
return out;
|
|
}
|
|
|
|
private:
|
|
//
|
|
// The caches for Bernoulli and tangent numbers, once allocated,
|
|
// these must NEVER EVER reallocate as it breaks our thread
|
|
// safety guarantees:
|
|
//
|
|
fixed_vector<T> bn, tn;
|
|
std::vector<T> m_intermediates;
|
|
// The value at which we know overflow has already occurred for the Bn:
|
|
std::size_t m_overflow_limit;
|
|
#if !defined(BOOST_HAS_THREADS)
|
|
int m_current_precision;
|
|
#elif defined(BOOST_MATH_NO_ATOMIC_INT)
|
|
boost::detail::lightweight_mutex m_mutex;
|
|
int m_current_precision;
|
|
#else
|
|
boost::detail::lightweight_mutex m_mutex;
|
|
atomic_counter_type m_counter, m_current_precision;
|
|
#endif
|
|
};
|
|
|
|
template <class T, class Policy>
|
|
inline bernoulli_numbers_cache<T, Policy>& get_bernoulli_numbers_cache()
|
|
{
|
|
//
|
|
// Force this function to be called at program startup so all the static variables
|
|
// get initailzed then (thread safety).
|
|
//
|
|
bernoulli_initializer<T, Policy>::force_instantiate();
|
|
static bernoulli_numbers_cache<T, Policy> data;
|
|
return data;
|
|
}
|
|
|
|
}}}
|
|
|
|
#endif // BOOST_MATH_BERNOULLI_DETAIL_HPP
|