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Add negative m for jacobi elliptic functions #88

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Add negative m for jacobi elliptic functions #88

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18 changes: 17 additions & 1 deletion include/xsf/cephes/ellpj.h
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Original file line number Diff line number Diff line change
Expand Up @@ -82,14 +82,30 @@ namespace cephes {
int i;

/* Check for special cases */
if (m < 0.0 || m > 1.0 || std::isnan(m)) {
if (m > 1.0 || std::isnan(m)) {
set_error("ellpj", SF_ERROR_DOMAIN, NULL);
*sn = std::numeric_limits<double>::quiet_NaN();
*cn = std::numeric_limits<double>::quiet_NaN();
*ph = std::numeric_limits<double>::quiet_NaN();
*dn = std::numeric_limits<double>::quiet_NaN();
return (-1);
}
/* Handle negative m by transformation (DLMF 22.17) */
if (m < 0.0) {
double m1 = -m / (1.0 - m);
double u1 = std::sqrt(1.0 - m) * u;
double sn_p, cn_p, dn_p, ph_p;

int result = ellpj(u1, m1, &sn_p, &cn_p, &dn_p, &ph_p);
if (result != 0)
return result;

*sn = sn_p / (std::sqrt(1.0 - m) * dn_p);
*cn = cn_p / dn_p;
*dn = 1.0 / dn_p;
*ph = std::atan2(*sn, *cn);
return (0);
}
if (m < 1.0e-9) {
t = std::sin(u);
b = std::cos(u);
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67 changes: 67 additions & 0 deletions tests/xsf_tests/test_ellpj.cpp
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@@ -0,0 +1,67 @@
#include "../testing_utils.h"
#include <iostream>
#include <tuple>
#include <xsf/cephes/ellpj.h>

TEST_CASE("ellpj negative m", "[ellpj][xsf_tests]") {
// u_values = [-10, -6, -2, 2, 6, 10]
// Reference values computed with mpmath

using test_case = std::tuple<double, double, double, double, double>;
// u, m, ref_sn, ref_cn, ref_dn

auto [u, m, ref_sn, ref_cn, ref_dn] = GENERATE(
// m = -2
test_case{-10.0, -2.0, -0.649677834014239, 0.760209650024628, 1.3579994757064},
test_case{-6.0, -2.0, -0.969931206391936, -0.243379240830198, 1.69750790580363},
test_case{-2.0, -2.0, -0.348621324159513, -0.937263662125694, 1.11493213036376},
test_case{2.0, -2.0, 0.348621324159513, -0.937263662125694, 1.11493213036376},
test_case{6.0, -2.0, 0.969931206391936, -0.243379240830198, 1.69750790580363},
test_case{10.0, -2.0, 0.649677834014239, 0.760209650024628, 1.3579994757064},

// m = -5
test_case{-10.0, -5.0, 0.495527059808153, -0.868592501117692, 1.49255999377263},
test_case{-6.0, -5.0, 0.279115494901804, -0.960257538635194, 1.17878212468267},
test_case{-2.0, -5.0, 0.0894599315921725, -0.995990421961739, 1.01981145159406},
test_case{2.0, -5.0, -0.0894599315921725, -0.995990421961739, 1.01981145159406},
test_case{6.0, -5.0, -0.279115494901804, -0.960257538635194, 1.17878212468267},
test_case{10.0, -5.0, -0.495527059808153, -0.868592501117692, 1.49255999377263},

// m = -10
test_case{-10.0, -10.0, -0.673927384474905, 0.738797590991479, 2.35409880749553},
test_case{-6.0, -10.0, 0.377239038384813, 0.926115925744991, 1.55662870358187},
test_case{-2.0, -10.0, 0.518272042082259, -0.855215815099256, 1.91991122087485},
test_case{2.0, -10.0, -0.518272042082259, -0.855215815099256, 1.91991122087485},
test_case{6.0, -10.0, -0.377239038384813, 0.926115925744991, 1.55662870358187},
test_case{10.0, -10.0, 0.673927384474905, 0.738797590991479, 2.35409880749553},

// m = -0.5
test_case{-10.0, -0.5, 0.993960849894643, 0.109735267242208, 1.22228437180619},
test_case{-6.0, -0.5, -0.333655198670901, 0.942695183184831, 1.02745457116121},
test_case{-2.0, -0.5, -0.766580871421719, -0.642147777050048, 1.13746345708987},
test_case{2.0, -0.5, 0.766580871421719, -0.642147777050048, 1.13746345708987},
test_case{6.0, -0.5, 0.333655198670901, 0.942695183184831, 1.02745457116121},
test_case{10.0, -0.5, -0.993960849894643, 0.109735267242208, 1.22228437180619}
);

const double rtol = 1e-8;

double sn, cn, dn, ph;
int result = xsf::cephes::ellpj(u, m, &sn, &cn, &dn, &ph);

REQUIRE(result == 0); // Should succeed

const auto rel_error_sn = xsf::extended_relative_error(sn, ref_sn);
const auto rel_error_cn = xsf::extended_relative_error(cn, ref_cn);
const auto rel_error_dn = xsf::extended_relative_error(dn, ref_dn);
const auto rel_error_ph = xsf::extended_relative_error(ph, std::atan2(ref_sn, ref_cn));

CAPTURE(u, m, sn, ref_sn, rtol, rel_error_sn);
CAPTURE(u, m, cn, ref_cn, rtol, rel_error_cn);
CAPTURE(u, m, dn, ref_dn, rtol, rel_error_dn);

REQUIRE(rel_error_sn <= rtol);
REQUIRE(rel_error_cn <= rtol);
REQUIRE(rel_error_dn <= rtol);
REQUIRE(rel_error_ph <= rtol);
}
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