diff options
Diffstat (limited to 'boost/math/special_functions/ellint_1.hpp')
| -rw-r--r-- | boost/math/special_functions/ellint_1.hpp | 14 |
1 files changed, 13 insertions, 1 deletions
diff --git a/boost/math/special_functions/ellint_1.hpp b/boost/math/special_functions/ellint_1.hpp index da16bc6f26..62a0bf3fde 100644 --- a/boost/math/special_functions/ellint_1.hpp +++ b/boost/math/special_functions/ellint_1.hpp @@ -103,10 +103,22 @@ T ellint_f_imp(T phi, T k, const Policy& pol) BOOST_MATH_INSTRUMENT_VARIABLE(rphi); } T sinp = sin(rphi); + sinp *= sinp; T cosp = cos(rphi); + cosp *= cosp; + T c = 1 / sinp; BOOST_MATH_INSTRUMENT_VARIABLE(sinp); BOOST_MATH_INSTRUMENT_VARIABLE(cosp); - result = s * sinp * ellint_rf_imp(T(cosp * cosp), T(1 - k * k * sinp * sinp), T(1), pol); + if(sinp > tools::min_value<T>()) + { + // + // Use http://dlmf.nist.gov/19.25#E5, note that + // c-1 simplifies to cot^2(rphi) which avoid cancellation: + // + result = rphi == 0 ? static_cast<T>(0) : static_cast<T>(s * ellint_rf_imp(T(cosp / sinp), T(c - k * k), c, pol)); + } + else + result = s * sin(rphi); BOOST_MATH_INSTRUMENT_VARIABLE(result); if(m != 0) { |