--- /dev/null
+// Copyright John Maddock 2012.
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_JACOBI_ELLIPTIC_HPP
+#define BOOST_MATH_JACOBI_ELLIPTIC_HPP
+
+#include <boost/math/tools/precision.hpp>
+#include <boost/math/tools/promotion.hpp>
+#include <boost/math/policies/error_handling.hpp>
+
+namespace boost{ namespace math{
+
+namespace detail{
+
+template <class T, class Policy>
+T jacobi_recurse(const T& x, const T& k, T anm1, T bnm1, unsigned N, T* pTn, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+ ++N;
+ T Tn;
+ T cn = (anm1 - bnm1) / 2;
+ T an = (anm1 + bnm1) / 2;
+ if(cn < policies::get_epsilon<T, Policy>())
+ {
+ Tn = ldexp(T(1), (int)N) * x * an;
+ }
+ else
+ Tn = jacobi_recurse<T>(x, k, an, sqrt(anm1 * bnm1), N, 0, pol);
+ if(pTn)
+ *pTn = Tn;
+ return (Tn + asin((cn / an) * sin(Tn))) / 2;
+}
+
+template <class T, class Policy>
+T jacobi_imp(const T& x, const T& k, T* cn, T* dn, const Policy& pol, const char* function)
+{
+ BOOST_MATH_STD_USING
+ if(k < 0)
+ {
+ *cn = policies::raise_domain_error<T>(function, "Modulus k must be positive but got %1%.", k, pol);
+ *dn = *cn;
+ return *cn;
+ }
+ if(k > 1)
+ {
+ T xp = x * k;
+ T kp = 1 / k;
+ T snp, cnp, dnp;
+ snp = jacobi_imp(xp, kp, &cnp, &dnp, pol, function);
+ *cn = dnp;
+ *dn = cnp;
+ return snp * kp;
+ }
+ //
+ // Special cases first:
+ //
+ if(x == 0)
+ {
+ *cn = *dn = 1;
+ return 0;
+ }
+ if(k == 0)
+ {
+ *cn = cos(x);
+ *dn = 1;
+ return sin(x);
+ }
+ if(k == 1)
+ {
+ *cn = *dn = 1 / cosh(x);
+ return tanh(x);
+ }
+ //
+ // Asymptotic forms from A&S 16.13:
+ //
+ if(k < tools::forth_root_epsilon<T>())
+ {
+ T su = sin(x);
+ T cu = cos(x);
+ T m = k * k;
+ *dn = 1 - m * su * su / 2;
+ *cn = cu + m * (x - su * cu) * su / 4;
+ return su - m * (x - su * cu) * cu / 4;
+ }
+ /* Can't get this to work to adequate precision - disabled for now...
+ //
+ // Asymptotic forms from A&S 16.15:
+ //
+ if(k > 1 - tools::root_epsilon<T>())
+ {
+ T tu = tanh(x);
+ T su = sinh(x);
+ T cu = cosh(x);
+ T sec = 1 / cu;
+ T kp = 1 - k;
+ T m1 = 2 * kp - kp * kp;
+ *dn = sec + m1 * (su * cu + x) * tu * sec / 4;
+ *cn = sec - m1 * (su * cu - x) * tu * sec / 4;
+ T sn = tu;
+ T sn2 = m1 * (x * sec * sec - tu) / 4;
+ T sn3 = (72 * x * cu + 4 * (8 * x * x - 5) * su - 19 * sinh(3 * x) + sinh(5 * x)) * sec * sec * sec * m1 * m1 / 512;
+ return sn + sn2 - sn3;
+ }*/
+ T T1;
+ T kc = 1 - k;
+ T k_prime = k < 0.5 ? T(sqrt(1 - k * k)) : T(sqrt(2 * kc - kc * kc));
+ T T0 = jacobi_recurse(x, k, T(1), k_prime, 0, &T1, pol);
+ *cn = cos(T0);
+ *dn = cos(T0) / cos(T1 - T0);
+ return sin(T0);
+}
+
+} // namespace detail
+
+template <class T, class U, class V, class Policy>
+inline typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn, V* pdn, const Policy&)
+{
+ BOOST_FPU_EXCEPTION_GUARD
+ typedef typename tools::promote_args<T>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ typedef typename policies::normalise<
+ Policy,
+ policies::promote_float<false>,
+ policies::promote_double<false>,
+ policies::discrete_quantile<>,
+ policies::assert_undefined<> >::type forwarding_policy;
+
+ static const char* function = "boost::math::jacobi_elliptic<%1%>(%1%)";
+
+ value_type sn, cn, dn;
+ sn = detail::jacobi_imp<value_type>(static_cast<value_type>(theta), static_cast<value_type>(k), &cn, &dn, forwarding_policy(), function);
+ if(pcn)
+ *pcn = policies::checked_narrowing_cast<result_type, Policy>(cn, function);
+ if(pdn)
+ *pdn = policies::checked_narrowing_cast<result_type, Policy>(dn, function);
+ return policies::checked_narrowing_cast<result_type, Policy>(sn, function);;
+}
+
+template <class T, class U, class V>
+inline typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn, V* pdn)
+{
+ return jacobi_elliptic(k, theta, pcn, pdn, policies::policy<>());
+}
+
+template <class U, class T, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ return jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), static_cast<result_type*>(0), static_cast<result_type*>(0), pol);
+}
+
+template <class U, class T>
+inline typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta)
+{
+ return jacobi_sn(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ result_type cn;
+ jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), &cn, static_cast<result_type*>(0), pol);
+ return cn;
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta)
+{
+ return jacobi_cn(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ result_type dn;
+ jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), static_cast<result_type*>(0), &dn, pol);
+ return dn;
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta)
+{
+ return jacobi_dn(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ result_type cn, dn;
+ jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), &cn, &dn, pol);
+ return cn / dn;
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta)
+{
+ return jacobi_cd(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ result_type cn, dn;
+ jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), &cn, &dn, pol);
+ return dn / cn;
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta)
+{
+ return jacobi_dc(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ return 1 / jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), static_cast<result_type*>(0), static_cast<result_type*>(0), pol);
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta)
+{
+ return jacobi_ns(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ result_type sn, dn;
+ sn = jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), static_cast<result_type*>(0), &dn, pol);
+ return sn / dn;
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta)
+{
+ return jacobi_sd(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ result_type sn, dn;
+ sn = jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), static_cast<result_type*>(0), &dn, pol);
+ return dn / sn;
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta)
+{
+ return jacobi_ds(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta, const Policy& pol)
+{
+ return 1 / jacobi_cn(k, theta, pol);
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta)
+{
+ return jacobi_nc(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta, const Policy& pol)
+{
+ return 1 / jacobi_dn(k, theta, pol);
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta)
+{
+ return jacobi_nd(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ result_type sn, cn;
+ sn = jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), &cn, static_cast<result_type*>(0), pol);
+ return sn / cn;
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta)
+{
+ return jacobi_sc(k, theta, policies::policy<>());
+}
+
+template <class T, class U, class Policy>
+inline typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta, const Policy& pol)
+{
+ typedef typename tools::promote_args<T, U>::type result_type;
+ result_type sn, cn;
+ sn = jacobi_elliptic(static_cast<result_type>(k), static_cast<result_type>(theta), &cn, static_cast<result_type*>(0), pol);
+ return cn / sn;
+}
+
+template <class T, class U>
+inline typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta)
+{
+ return jacobi_cs(k, theta, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_JACOBI_ELLIPTIC_HPP
projects / rsem.git / blobdiff