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Correct ellint_2 for N * PI / 2 phi argument. #1378

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Merged
jzmaddock merged 2 commits into from
Mar 12, 2026
Merged

Correct ellint_2 for N * PI / 2 phi argument. #1378

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6f59f38
Correct ellint_2 for N * PI / 2 phi argument.
jzmaddock Mar 11, 2026
c793e1c
Ellint2: Simplify fix.
jzmaddock Mar 12, 2026
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2 changes: 1 addition & 1 deletion include/boost/math/special_functions/ellint_2.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED T ellint_e_imp(T phi, T k, const Policy& pol)
rphi = constants::half_pi<T>() - rphi;
}
T k2 = k * k;
if(boost::math::pow<3>(rphi) * k2 / 6 < tools::epsilon<T>() * fabs(rphi))
if(boost::math::pow<3>(rphi) * k2 / 6 <= tools::epsilon<T>() * fabs(rphi))
{
// See http://functions.wolfram.com/EllipticIntegrals/EllipticE2/06/01/03/0001/
result = s * rphi;
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6 changes: 5 additions & 1 deletion test/test_ellint_2.hpp
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Expand Up @@ -97,7 +97,7 @@ void test_spots(T, const char* type_name)
// called a second time.
//
#ifndef TEST_UDT
static const std::array<std::array<T, 3>, 28> data1 = {{
static const std::array<std::array<T, 3>, 31> data1 = {{
{{ SC_(0.0), SC_(0.0), SC_(0.0) }},
{{ SC_(-10.0), SC_(0.0), SC_(-10.0) }},
{{ SC_(-1.0), SC_(-1.0), SC_(-0.84147098480789650665250232163029899962256306079837) }},
Expand Down Expand Up @@ -127,6 +127,10 @@ void test_spots(T, const char* type_name)
{{ -2 * boost::math::constants::pi<T>(), SC_(1.0), SC_(-4.0) }},
{{ -(20 * boost::math::constants::pi<T>()) / 21, SC_(1.0), SC_(-1.85095773382382555307064528472278244309033056100177750424044959888147151556780639619867349409562910808166870200808) }},
{{ -(20 * boost::math::constants::pi<T>()) / 19, SC_(1.0), SC_(-2.16459459028073389414365205908793841951217248335965412335147127404907690285247170629778731438009399303864259295133) }},
// Test at n * pi / 2, see https://github.com/boostorg/math/issues/1377
{{ boost::math::constants::half_pi<T>(), SC_(0.25), boost::math::ellint_2(static_cast<T>(0.25)) }},
{{ 3 * boost::math::constants::half_pi<T>(), SC_(0.25), 3 * boost::math::ellint_2(static_cast<T>(0.25)) }},
{{ 6 * boost::math::constants::half_pi<T>(), SC_(0.25), 6 * boost::math::ellint_2(static_cast<T>(0.25)) }},
}};

do_test_ellint_e2<T>(data1, type_name, "Elliptic Integral E: Mathworld Data");
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