diff --git a/include/boost/math/special_functions/detail/hypergeometric_1F1_bessel.hpp b/include/boost/math/special_functions/detail/hypergeometric_1F1_bessel.hpp index 7ffcdd8a0..da7e09cec 100644 --- a/include/boost/math/special_functions/detail/hypergeometric_1F1_bessel.hpp +++ b/include/boost/math/special_functions/detail/hypergeometric_1F1_bessel.hpp @@ -109,7 +109,7 @@ // function for 13_3_7 evaluation template - inline T hypergeometric_1F1_13_3_7_series(const T& a, const T& b, const T& z, const Policy& pol, const char* function) + inline T hypergeometric_1F1_13_3_7_series(const T& a, const T& b, const T& z, const Policy& pol, const char* function, int& log_scaling) { BOOST_MATH_STD_USING @@ -156,13 +156,13 @@ } catch (const std::exception&) { - // The bessel functions can overflow, use a chacked series in that case: - return hypergeometric_1F1_checked_series_impl(a, b, z, pol); + // The bessel functions can overflow, use a checked series in that case: + return hypergeometric_1F1_checked_series_impl(a, b, z, pol, log_scaling); } if (!(boost::math::isfinite)(result)) { // as above: - return hypergeometric_1F1_checked_series_impl(a, b, z, pol); + return hypergeometric_1F1_checked_series_impl(a, b, z, pol, log_scaling); } boost::math::policies::check_series_iterations("boost::math::hypergeometric_1F1_13_3_7_series<%1%>(%1%,%1%,%1%)", max_iter, pol); diff --git a/include/boost/math/special_functions/detail/hypergeometric_1F1_recurrence.hpp b/include/boost/math/special_functions/detail/hypergeometric_1F1_recurrence.hpp index 29280f27f..5a30f0d0d 100644 --- a/include/boost/math/special_functions/detail/hypergeometric_1F1_recurrence.hpp +++ b/include/boost/math/special_functions/detail/hypergeometric_1F1_recurrence.hpp @@ -206,6 +206,50 @@ return a < -10; // TODO: make dependent on precision } + template + inline T hypergeometric_1F1_imp(const T& a, const T& b, const T& z, const Policy& pol, int& log_scaling); + + template + T hypergeometric_1F1_fwd_on_b_imp(const T& a, const T& b, const T& z, const Policy& pol, int& log_scaling) + { + BOOST_MATH_STD_USING // modf, fabs + + int integer_part = 1 + itrunc(ceil(fabs(a) - b)); + T bk = b + integer_part; + + T first = boost::math::detail::hypergeometric_1F1_imp(a, bk, z, pol, log_scaling); + --bk; + int log_scaling2 = 0; + T second = boost::math::detail::hypergeometric_1F1_imp(a, bk, z, pol, log_scaling2); + + if (log_scaling2 != log_scaling) + { + second *= exp(log_scaling2 - log_scaling); + } + + //std::cout << first * exp(boost::multiprecision::mpfr_float(log_scaling)) << std::endl; + //std::cout << second * exp(boost::multiprecision::mpfr_float(log_scaling)) << std::endl; + + if ((fabs(first) > 1.0e3) || (fabs(first) < 1.0e-3)) + { + int rescaling = itrunc(floor(log(fabs(first)))); + T scale = exp(-rescaling); + + first *= scale; + second *= scale; + log_scaling += rescaling; + } + + //std::cout << first * exp(boost::multiprecision::mpfr_float(log_scaling)) << std::endl; + //std::cout << second * exp(boost::multiprecision::mpfr_float(log_scaling)) << std::endl; + + boost::math::detail::hypergeometric_1F1_recurrence_b_coefficients s(a, bk, z); + + return boost::math::tools::solve_recurrence_relation_backward(s, static_cast(integer_part), first, second); + } + + + } } } // namespaces #endif // BOOST_HYPERGEOMETRIC_1F1_RECURRENCE_HPP_ diff --git a/include/boost/math/special_functions/detail/hypergeometric_asym.hpp b/include/boost/math/special_functions/detail/hypergeometric_asym.hpp index 0077821be..e07428ed6 100644 --- a/include/boost/math/special_functions/detail/hypergeometric_asym.hpp +++ b/include/boost/math/special_functions/detail/hypergeometric_asym.hpp @@ -56,7 +56,7 @@ log_scaling -= e; prefix /= s * exp(t - e); - return prefix * boost::math::detail::hypergeometric_2F0_imp(1 - a, b - a, 1 / z, pol, true); + return prefix * boost::math::detail::hypergeometric_2F0_imp(T(1 - a), T(b - a), T(1 / z), pol, true); } diff --git a/include/boost/math/special_functions/detail/hypergeometric_pFq_checked_series.hpp b/include/boost/math/special_functions/detail/hypergeometric_pFq_checked_series.hpp index 32ee353e8..149b0a157 100644 --- a/include/boost/math/special_functions/detail/hypergeometric_pFq_checked_series.hpp +++ b/include/boost/math/special_functions/detail/hypergeometric_pFq_checked_series.hpp @@ -12,7 +12,7 @@ namespace boost { namespace math { namespace detail { template - std::pair hypergeometric_pFq_checked_series_impl(const Seq& aj, const Seq& bj, const Real& z, const Policy& pol, const Terminal& termination) + std::pair hypergeometric_pFq_checked_series_impl(const Seq& aj, const Seq& bj, const Real& z, const Policy& pol, const Terminal& termination, int& log_scale) { using std::abs; Real result = 1; @@ -20,6 +20,10 @@ Real term = 1; Real tol = boost::math::policies::get_epsilon(); boost::uintmax_t k = 0; + int log_scaling_factor = boost::math::itrunc(boost::math::tools::log_max_value()) - 2; + Real scaling_factor = exp(log_scaling_factor); + Real upper_limit(sqrt(boost::math::tools::max_value())); + Real lower_limit(1 / upper_limit); while (!termination(k)) { @@ -47,6 +51,22 @@ term /= k; result += term; abs_result += abs(term); + + if (fabs(result) >= upper_limit) + { + result /= scaling_factor; + abs_result /= scaling_factor; + term /= scaling_factor; + log_scale += log_scaling_factor; + } + if (fabs(result) < lower_limit) + { + result *= scaling_factor; + abs_result *= scaling_factor; + term *= scaling_factor; + log_scale -= log_scaling_factor; + } + if (abs(result * tol) > abs(term)) break; if (abs_result * tol > abs(result)) @@ -69,11 +89,11 @@ }; template - Real hypergeometric_pFq_checked_series_impl(const Seq& aj, const Seq& bj, const Real& z, const Policy& pol) + Real hypergeometric_pFq_checked_series_impl(const Seq& aj, const Seq& bj, const Real& z, const Policy& pol, int& log_scale) { using std::abs; iteration_terminator term(boost::math::policies::get_max_series_iterations()); - std::pair result = hypergeometric_pFq_checked_series_impl(aj, bj, z, pol, term); + std::pair result = hypergeometric_pFq_checked_series_impl(aj, bj, z, pol, term, log_scale); // // Check to see how many digits we've lost, if it's more than half, raise an evaluation error - // this is an entirely arbitrary cut off, but not unreasonable. @@ -86,11 +106,11 @@ } template - inline Real hypergeometric_1F1_checked_series_impl(const Real& a, const Real& b, const Real& z, const Policy& pol) + inline Real hypergeometric_1F1_checked_series_impl(const Real& a, const Real& b, const Real& z, const Policy& pol, int& log_scale) { boost::array aj = { a }; boost::array bj = { b }; - return hypergeometric_pFq_checked_series_impl(aj, bj, z, pol); + return hypergeometric_pFq_checked_series_impl(aj, bj, z, pol, log_scale); } } } } // namespaces diff --git a/include/boost/math/special_functions/detail/hypergeometric_series.hpp b/include/boost/math/special_functions/detail/hypergeometric_series.hpp index 393f403b6..0f037a9f4 100644 --- a/include/boost/math/special_functions/detail/hypergeometric_series.hpp +++ b/include/boost/math/special_functions/detail/hypergeometric_series.hpp @@ -208,6 +208,31 @@ return detail::sum_pFq_series(s, pol); } + template + inline T log_pochhammer(T z, unsigned n, const Policy pol, int* s = 0) + { + if (z < 0) + { + if (n < -z) + { + if(s) + *s = (n & 1 ? -1 : 1); + return log_pochhammer(T(-z - n + 1), n, pol); + } + else + { + int cross = itrunc(ceil(-z)); + return log_pochhammer(T(-z - cross + 1), cross, pol, s) + log_pochhammer(T(cross + z), n - cross, pol); + } + } + else + { + if(s) + *s = 1; + return lgamma(z + n, pol) - lgamma(z, pol); + } + } + template inline T hypergeometric_1F1_generic_series(const T& a, const T& b, const T& z, const Policy& pol, int& log_scaling, const char* function) { @@ -217,6 +242,8 @@ unsigned n = 0; int log_scaling_factor = boost::math::itrunc(boost::math::tools::log_max_value()) - 2; T scaling_factor = exp(log_scaling_factor); + T term_m1 = 0; + int local_scaling = 0; do { @@ -226,19 +253,108 @@ sum /= scaling_factor; term /= scaling_factor; log_scaling += log_scaling_factor; + local_scaling += log_scaling_factor; } if (fabs(sum) < lower_limit) { sum *= scaling_factor; term *= scaling_factor; log_scaling -= log_scaling_factor; + local_scaling -= log_scaling_factor; } + term_m1 = term; term *= (((a + n) / ((b + n) * (n + 1))) * z); if (n > boost::math::policies::get_max_series_iterations()) return boost::math::policies::raise_evaluation_error(function, "Series did not converge, best value is %1%", sum, pol); ++n; diff = fabs(term / sum); - } while (diff > boost::math::policies::get_epsilon()); + } while ((diff > boost::math::policies::get_epsilon()) || (fabs(term_m1) < fabs(term))); + + if (b + n < 0) + { + if ((a < 0) && (floor(a) == a) && (a > b)) + return sum; // b will never cross the origin! + // + // b hasn't crossed the origin yet and the series may spring back into life at that point + // so we need to jump forward to that term and then evaluate forwards and backwards from there: + // + unsigned s = itrunc(-b); + unsigned backstop = n; + int s1, s2; + T t1 = log_pochhammer(a, s, pol, &s1); + T t2 = log_pochhammer(b, s, pol, &s2); + term = t1 - t2; + t1 = lgamma(T(s + 1), pol); + term -= t1; + term += s * log(fabs(z)); + if(z < 0) + s1 *= (s & 1 ? -1 : 1); + term -= local_scaling; + if (term > -tools::log_max_value()) + { + if (term > 10) + { + int scale = itrunc(floor(term)); + term -= scale; + log_scaling += scale; + sum *= exp(T(-scale)); + } + term = s1 * s2 * exp(term); + n = s; + T term0 = term; + do + { + sum += term; + if (fabs(sum) >= upper_limit) + { + sum /= scaling_factor; + term /= scaling_factor; + log_scaling += log_scaling_factor; + term0 /= scaling_factor; + } + if (fabs(sum) < lower_limit) + { + sum *= scaling_factor; + term *= scaling_factor; + log_scaling -= log_scaling_factor; + term0 *= scaling_factor; + } + term_m1 = term; + term *= (((a + n) / ((b + n) * (n + 1))) * z); + //if (n > boost::math::policies::get_max_series_iterations()) + // return boost::math::policies::raise_evaluation_error(function, "Series did not converge, best value is %1%", sum, pol); + ++n; + diff = fabs(term / sum); + } while ((diff > boost::math::policies::get_epsilon()) || (fabs(term) > fabs(term_m1))); + // + // Now go backwards as well: + // + n = s; + term = term0; + do + { + --n; + if (n == backstop) + break; + term_m1 = term; + term /= (((a + n) / ((b + n) * (n + 1))) * z); + sum += term; + if (fabs(sum) >= upper_limit) + { + sum /= scaling_factor; + term /= scaling_factor; + log_scaling += log_scaling_factor; + } + if (fabs(sum) < lower_limit) + { + sum *= scaling_factor; + term *= scaling_factor; + log_scaling -= log_scaling_factor; + } + diff = fabs(term / sum); + } while ((diff > boost::math::policies::get_epsilon()) || (fabs(term) > fabs(term_m1))); + } + } return sum; } diff --git a/include/boost/math/special_functions/hypergeometric_1F1.hpp b/include/boost/math/special_functions/hypergeometric_1F1.hpp index f18dd06d1..904cb8e5f 100644 --- a/include/boost/math/special_functions/hypergeometric_1F1.hpp +++ b/include/boost/math/special_functions/hypergeometric_1F1.hpp @@ -39,7 +39,7 @@ namespace boost { namespace math { namespace detail { } template - inline T hypergeometric_1F1_imp(const T& a, const T& b, const T& z, const Policy& pol, int& log_scaling) + T hypergeometric_1F1_imp(const T& a, const T& b, const T& z, const Policy& pol, int& log_scaling) { BOOST_MATH_STD_USING // exp, fabs, sqrt @@ -83,9 +83,11 @@ namespace boost { namespace math { namespace detail { return exp(z); if (b - a == b) return 1; - - // asymptotic expansion - // check region + // + // Asymptotic expansion for large z + // TODO: check region for higher precision types. + // Use recurrence relations to move to this region when a and b are also large. + // if (detail::hypergeometric_1F1_asym_region(a, b, z, pol)) { return hypergeometric_1F1_asym_large_z_series(a, b, z, pol, log_scaling); @@ -115,13 +117,19 @@ namespace boost { namespace math { namespace detail { // Without this we get into an area where the series don't converge if b - a ~ b return hypergeometric_1F1_backward_recurrence_for_negative_a(a, b, z, pol, function); } + if ((a > 0) && (b + 1 < a)) + { + // Moving to a larger b value will allow us to apply Jummer's relation below: + return hypergeometric_1F1_fwd_on_b_imp(a, b, z, pol, log_scaling); + } // Let's otherwise make z positive (almost always) // by Kummer's transformation // (we also don't transform if z belongs to [-1,0]) int scaling = itrunc(z); + T r = exp(z - scaling) * detail::hypergeometric_1F1_imp(b_minus_a, b, -z, pol, log_scaling); log_scaling += scaling; - return exp(z - scaling) * detail::hypergeometric_1F1_imp(b_minus_a, b, -z, pol, log_scaling); + return r; } // // Check for initial divergence: @@ -168,13 +176,13 @@ namespace boost { namespace math { namespace detail { if ((a == ceil(a)) && !b_is_negative_and_greater_than_z) return detail::hypergeometric_1F1_backward_recurrence_for_negative_a(a, b, z, pol, function); else if ((z > 0) && (2 * (z * (b - (2 * a))) > 0) && (b > -100)) // TODO: see when this methd is bad in opposite to usual taylor - return detail::hypergeometric_1F1_13_3_7_series(a, b, z, pol, function); + return detail::hypergeometric_1F1_13_3_7_series(a, b, z, pol, function, log_scaling); else if (b < a) return detail::hypergeometric_1F1_backward_recurrence_for_negative_b(a, b, z, pol); } // If we get here, then we've run out of methods to try, use the checked series which will // raise an error if the result is garbage: - return hypergeometric_1F1_checked_series_impl(a, b, z, pol); + return hypergeometric_1F1_checked_series_impl(a, b, z, pol, log_scaling); } return detail::hypergeometric_1F1_generic_series(a, b, z, pol, log_scaling, function); diff --git a/test/hypergeometric_1F1_big.ipp b/test/hypergeometric_1F1_big.ipp index e21322b86..2b75cb194 100644 --- a/test/hypergeometric_1F1_big.ipp +++ b/test/hypergeometric_1F1_big.ipp @@ -1,7 +1,7 @@ #ifndef SC_ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif - static const boost::array, 2328-3> hypergeometric_1F1_big = {{ + static const boost::array, 2396 - 4> hypergeometric_1F1_big = {{ { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.2220855000000000000000000000000000000000e+06), SC_(-1.0437607421875000000000000000000000000000e+03), SC_(5.7183779146807201355480824984892132235960e-303) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.2220855000000000000000000000000000000000e+06), SC_(-1.5873352050781250000000000000000000000000e+01), SC_(2.5361996854293809244896531977363790923005e-05) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.2220855000000000000000000000000000000000e+06), SC_(-1.2110849638702347874641418457031250000000e-05), SC_(9.9999192613200886724554310382028215474902e-01) }, @@ -20,6 +20,7 @@ { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-2.0321554687500000000000000000000000000000e+04), SC_(1.1417195314167294384333217749372124671936e-12), SC_(1.0000000000457733688396162733887274883634e+00) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-2.0321554687500000000000000000000000000000e+04), SC_(1.2110846000723540782928466796875000000000e-05), SC_(1.0004856611588072199743182877998224950270e+00) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-2.0321554687500000000000000000000000000000e+04), SC_(1.5873352050781250000000000000000000000000e+01), SC_(6.0889904945622204539981795208905638705257e+280) }, + //{ SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.3586878906250000000000000000000000000000e+04), SC_(-1.5873352050781250000000000000000000000000e+01), SC_(4.9489925464971372677922628162736666342744e-401) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.3586878906250000000000000000000000000000e+04), SC_(-1.2110849638702347874641418457031250000000e-05), SC_(9.9927404853401060452253718538570738021733e-01) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.3586878906250000000000000000000000000000e+04), SC_(-1.1417199650975984326350953779183328151703e-12), SC_(9.9999999993153789197646762190948811399195e-01) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.3586878906250000000000000000000000000000e+04), SC_(-2.7629261207602954767400179815809657975825e-31), SC_(9.9999999999999999999999999998343238689613e-01) }, @@ -32,12 +33,12 @@ { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.2525131835937500000000000000000000000000e+03), SC_(2.7629251803648148189100116065917360197859e-31), SC_(1.0000000000000000000000000001797203249755e+00) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.2525131835937500000000000000000000000000e+03), SC_(1.1417195314167294384333217749372124671936e-12), SC_(1.0000000007426556707058694021282093761226e+00) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.2525131835937500000000000000000000000000e+03), SC_(1.2110846000723540782928466796875000000000e-05), SC_(1.0079088926137324761328829498026828704710e+00) }, - { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.9048027038574218750000000000000000000000e+01), SC_(-1.2110849638702347874641418457031250000000e-05), SC_(5.9998117541687286664272909666416178234204e-01) }, + { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.9048027038574218750000000000000000000000e+01), SC_(-1.2110849638702347874641418457031250000000e-05), SC_(5.9998117541687286664272909666416178234200e-01) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.9048027038574218750000000000000000000000e+01), SC_(-1.1417199650975984326350953779183328151703e-12), SC_(9.9999995116626275467696724155639930307403e-01) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.9048027038574218750000000000000000000000e+01), SC_(-2.7629261207602954767400179815809657975825e-31), SC_(9.9999999999999999999999998818239009467894e-01) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.9048027038574218750000000000000000000000e+01), SC_(2.7629251803648148189100116065917360197859e-31), SC_(1.0000000000000000000000000118176058830539e+00) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.9048027038574218750000000000000000000000e+01), SC_(1.1417195314167294384333217749372124671936e-12), SC_(1.0000000488337212127525404244395189345121e+00) }, - { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.9048027038574218750000000000000000000000e+01), SC_(1.2110846000723540782928466796875000000000e-05), SC_(1.6917446896910904323205164624667509881678e+00) }, + { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.9048027038574218750000000000000000000000e+01), SC_(1.2110846000723540782928466796875000000000e-05), SC_(1.6917446896910904323205164624667509881679e+00) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.4533019566442817449569702148437500000000e-05), SC_(-1.2110849638702347874641418457031250000000e-05), SC_(-1.7243402644277887526870971660149662928095e+07) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.4533019566442817449569702148437500000000e-05), SC_(-1.1417199650975984326350953779183328151703e-12), SC_(9.3599493898768427435547004338219380315698e-01) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(-1.4533019566442817449569702148437500000000e-05), SC_(-2.7629261207602954767400179815809657975825e-31), SC_(9.9999999999999999998451098534762550169493e-01) }, @@ -92,6 +93,7 @@ { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(1.3586878906250000000000000000000000000000e+04), SC_(2.7629251803648148189100116065917360197859e-31), SC_(9.9999999999999999999999999998343239253512e-01) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(1.3586878906250000000000000000000000000000e+04), SC_(1.1417195314167294384333217749372124671936e-12), SC_(9.9999999993153791798171147643737431372971e-01) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(1.3586878906250000000000000000000000000000e+04), SC_(1.2110846000723540782928466796875000000000e-05), SC_(9.9927404871321226955822674865932639293072e-01) }, + { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(1.3586878906250000000000000000000000000000e+04), SC_(1.5873352050781250000000000000000000000000e+01), SC_(1.9976990618127286269329812204620520231089e-430) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(2.0321546875000000000000000000000000000000e+04), SC_(-1.5873352050781250000000000000000000000000e+01), SC_(1.3236571724099524262453202262396985329438e+272) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(2.0321546875000000000000000000000000000000e+04), SC_(-1.2110849638702347874641418457031250000000e-05), SC_(1.0004856614798787227470718859242077657990e+00) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(2.0321546875000000000000000000000000000000e+04), SC_(-1.1417199650975984326350953779183328151703e-12), SC_(1.0000000000457734038238893827099919544759e+00) }, @@ -110,8 +112,6 @@ { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(1.2220855000000000000000000000000000000000e+06), SC_(1.2110846000723540782928466796875000000000e-05), SC_(9.9999192613443411377567520463511081490478e-01) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(1.2220855000000000000000000000000000000000e+06), SC_(1.5873352050781250000000000000000000000000e+01), SC_(2.5359672900058277225815544067207713318427e-05) }, { SC_(-8.1472375000000000000000000000000000000000e+05), SC_(1.2220855000000000000000000000000000000000e+06), SC_(1.0437607421875000000000000000000000000000e+03), SC_(3.8451190975320878112717756382751849224523e-303) }, - { SC_(-1.3547703125000000000000000000000000000000e+04), SC_(-1.2220855000000000000000000000000000000000e+06), SC_(-1.6934625000000000000000000000000000000000e+04), SC_(8.0360476724709289524417834160784978041906e-83) }, - { SC_(-1.3547703125000000000000000000000000000000e+04), SC_(-1.2220855000000000000000000000000000000000e+06), SC_(-1.1322402343750000000000000000000000000000e+04), SC_(1.7274565045609195826148094337853809013570e-55) }, { SC_(-1.3547703125000000000000000000000000000000e+04), SC_(-1.2220855000000000000000000000000000000000e+06), SC_(-1.0437607421875000000000000000000000000000e+03), SC_(9.3912404849519973822063976591261065618658e-06) }, { SC_(-1.3547703125000000000000000000000000000000e+04), SC_(-1.2220855000000000000000000000000000000000e+06), SC_(-1.5873352050781250000000000000000000000000e+01), SC_(8.3864420120700820282469891300407306639301e-01) }, { SC_(-1.3547703125000000000000000000000000000000e+04), 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SC_(-2.7629261207602954767400179815809657975825e-31), SC_(9.9999999999999999999999999998343239197994e-01) }, diff --git a/tools/hyp_1f1_big_data.cpp b/tools/hyp_1f1_big_data.cpp index 29d4c0f86..1bd79b251 100644 --- a/tools/hyp_1f1_big_data.cpp +++ b/tools/hyp_1f1_big_data.cpp @@ -23,6 +23,7 @@ using namespace std; using namespace boost::multiprecision; typedef mpfi_float_1000 mpfi_type; + mp_t hypergeometric_1f1_generic_series(mp_t a_, mp_t b_, mp_t z_) { using namespace boost::math::tools; @@ -30,7 +31,7 @@ mp_t hypergeometric_1f1_generic_series(mp_t a_, mp_t b_, mp_t z_) using namespace std; using namespace boost::multiprecision; - mpfi_type a(a_), b(b_), z(z_), sum(0), term(1), diff; + mpfi_type a(a_), b(b_), z(z_), sum(0), term(1), diff, term0(0); unsigned n = 0; bool cont = true; @@ -40,6 +41,8 @@ mp_t hypergeometric_1f1_generic_series(mp_t a_, mp_t b_, mp_t z_) else max_n = 10000000; + mpfi_type overflow_limit("1.189731495357231765e+4900"); // a bit less than LDBL_MAX for extended long doubles. + do { sum += term; @@ -51,12 +54,13 @@ mp_t hypergeometric_1f1_generic_series(mp_t a_, mp_t b_, mp_t z_) std::cout << "Aborting series evaluation due to too many iterations...\n"; throw evaluation_error(""); } - if (fabs(upper(sum)) > std::numeric_limits::max()) + if (fabs(upper(sum)) > overflow_limit) { std::cout << "Aborting series evaluation due to over large sum...\n"; throw evaluation_error(""); } - cont = (fabs(upper(diff)) > 1e-40) || (b + n < 200); + cont = (fabs(upper(diff)) > 1e-40) || (b + n < 0) || (fabs(term0) < fabs(term)); + term0 = term; //std::cout << upper(term) << " " << upper(sum) << " " << upper(diff) << " " << cont << std::endl; } while (cont);