PR libstdc++/83566 - cyl_bessel_j returns wrong result for x>1000
2018-11-16 Michele Pezzutti <mpezz@tiscali.it> Edward Smith-Rowland <3dw4rd@verizon.net> PR libstdc++/83566 - cyl_bessel_j returns wrong result for x>1000 for high orders. * include/tr1/bessel_function.tcc: Perform no fewer than nu/2 iterations of the asymptotic series (nu is the Bessel order). * testsuite/tr1/5_numerical_facilities/special_functions/ 09_cyl_bessel_j/check_value.cc: Add tests at nu=100, 1000<=x<=2000. * testsuite/tr1/5_numerical_facilities/special_functions/ 11_cyl_neumann/check_value.cc: Ditto. * testsuite/special_functions/08_cyl_bessel_j/check_value.cc: Ditto. * testsuite/special_functions/10_cyl_neumann/check_value.cc: Ditto. Co-Authored-By: Edward Smith-Rowland <3dw4rd@verizon.net> From-SVN: r266252
This commit is contained in:
Michele Pezzutti
Edward Smith-Rowland
parent
cb40e8071e
commit
bee39274cb
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@ -1,3 +1,17 @@
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2018-11-18 Michele Pezzutti <mpezz@tiscali.it>
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Edward Smith-Rowland <3dw4rd@verizon.net>
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PR libstdc++/83566 - cyl_bessel_j returns wrong result for x>1000
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for high orders.
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* include/tr1/bessel_function.tcc: Perform no fewer than nu/2 iterations
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of the asymptotic series (nu is the Bessel order).
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* testsuite/tr1/5_numerical_facilities/special_functions/
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09_cyl_bessel_j/check_value.cc: Add tests at nu=100, 1000<=x<=2000.
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* testsuite/tr1/5_numerical_facilities/special_functions/
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11_cyl_neumann/check_value.cc: Ditto.
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* testsuite/special_functions/08_cyl_bessel_j/check_value.cc: Ditto.
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* testsuite/special_functions/10_cyl_neumann/check_value.cc: Ditto.
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2018-11-17 Jonathan Wakely <jwakely@redhat.com>
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Implement std::pmr::synchronized_pool_resource
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@ -27,6 +27,10 @@
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* Do not attempt to use it directly. @headername{tr1/cmath}
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*/
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/* __cyl_bessel_jn_asymp adapted from GNU GSL version 2.4 specfunc/bessel_j.c
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* Copyright (C) 1996-2003 Gerard Jungman
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*/
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//
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// ISO C++ 14882 TR1: 5.2 Special functions
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//
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@ -358,24 +362,51 @@ namespace tr1
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void
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__cyl_bessel_jn_asymp(_Tp __nu, _Tp __x, _Tp & __Jnu, _Tp & __Nnu)
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{
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const _Tp __mu = _Tp(4) * __nu * __nu;
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const _Tp __mum1 = __mu - _Tp(1);
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const _Tp __mum9 = __mu - _Tp(9);
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const _Tp __mum25 = __mu - _Tp(25);
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const _Tp __mum49 = __mu - _Tp(49);
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const _Tp __xx = _Tp(64) * __x * __x;
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const _Tp __P = _Tp(1) - __mum1 * __mum9 / (_Tp(2) * __xx)
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* (_Tp(1) - __mum25 * __mum49 / (_Tp(12) * __xx));
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const _Tp __Q = __mum1 / (_Tp(8) * __x)
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* (_Tp(1) - __mum9 * __mum25 / (_Tp(6) * __xx));
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const _Tp __mu = _Tp(4) * __nu * __nu;
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const _Tp __8x = _Tp(8) * __x;
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_Tp __P = _Tp(0);
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_Tp __Q = _Tp(0);
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_Tp __k = _Tp(0);
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_Tp __term = _Tp(1);
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int __epsP = 0;
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int __epsQ = 0;
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_Tp __eps = std::numeric_limits<_Tp>::epsilon();
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do
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{
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__term *= (__k == 0
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? _Tp(1)
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: -(__mu - (2 * __k - 1) * (2 * __k - 1)) / (__k * __8x));
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__epsP = std::abs(__term) < __eps * std::abs(__P);
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__P += __term;
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__k++;
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__term *= (__mu - (2 * __k - 1) * (2 * __k - 1)) / (__k * __8x);
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__epsQ = std::abs(__term) < __eps * std::abs(__Q);
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__Q += __term;
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if (__epsP && __epsQ && __k > (__nu / 2.))
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break;
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__k++;
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}
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while (__k < 1000);
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const _Tp __chi = __x - (__nu + _Tp(0.5L))
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* __numeric_constants<_Tp>::__pi_2();
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* __numeric_constants<_Tp>::__pi_2();
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const _Tp __c = std::cos(__chi);
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const _Tp __s = std::sin(__chi);
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const _Tp __coef = std::sqrt(_Tp(2)
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/ (__numeric_constants<_Tp>::__pi() * __x));
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__Jnu = __coef * (__c * __P - __s * __Q);
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__Nnu = __coef * (__s * __P + __c * __Q);
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@ -698,6 +698,39 @@ data026[21] =
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};
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const double toler026 = 1.0000000000000006e-11;
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// Test data for nu=100.0000000000000000
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// max(|f - f_GSL|): 3.9438938226332709e-14 at index 19
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// max(|f - f_GSL| / |f_GSL|): 2.0193411077170867e-11
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// mean(f - f_GSL): 1.6682360684660055e-15
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// variance(f - f_GSL): 5.3274331668346898e-28
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// stddev(f - f_GSL): 2.3081232997469372e-14
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const testcase_cyl_bessel_j<double>
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data027[21] =
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{
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{ 1.1676135007789573e-02, 100.0000000000000000, 1000.0000000000000000, 0.0 },
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{ -1.1699854778025796e-02, 100.0000000000000000, 1100.0000000000000000, 0.0 },
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{ -2.2801483405083697e-02, 100.0000000000000000, 1200.0000000000000000, 0.0 },
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{ -1.6973500787373915e-02, 100.0000000000000000, 1300.0000000000000000, 0.0 },
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{ -1.4154528803481308e-03, 100.0000000000000000, 1400.0000000000000000, 0.0 },
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{ 1.3333726584495232e-02, 100.0000000000000000, 1500.0000000000000000, 0.0 },
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{ 1.9802562020148559e-02, 100.0000000000000000, 1600.0000000000000000, 0.0 },
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{ 1.6129771279838816e-02, 100.0000000000000000, 1700.0000000000000000, 0.0 },
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{ 5.3753369281536031e-03, 100.0000000000000000, 1800.0000000000000000, 0.0 },
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{ -6.9238868725645785e-03, 100.0000000000000000, 1900.0000000000000000, 0.0 },
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{ -1.5487871720069789e-02, 100.0000000000000000, 2000.0000000000000000, 0.0 },
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{ -1.7275186717671070e-02, 100.0000000000000000, 2100.0000000000000000, 0.0 },
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{ -1.2233030525173150e-02, 100.0000000000000000, 2200.0000000000000000, 0.0 },
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{ -2.8518508672241900e-03, 100.0000000000000000, 2300.0000000000000000, 0.0 },
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{ 7.0784372270289329e-03, 100.0000000000000000, 2400.0000000000000000, 0.0 },
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{ 1.3955367586928166e-02, 100.0000000000000000, 2500.0000000000000000, 0.0 },
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{ 1.5574059842493392e-02, 100.0000000000000000, 2600.0000000000000000, 0.0 },
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{ 1.1718043044647556e-02, 100.0000000000000000, 2700.0000000000000000, 0.0 },
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{ 4.0320953231285607e-03, 100.0000000000000000, 2800.0000000000000000, 0.0 },
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{ -4.6895111783053977e-03, 100.0000000000000000, 2900.0000000000000000, 0.0 },
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{ -1.1507715400035966e-02, 100.0000000000000000, 3000.0000000000000000, 0.0 },
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};
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const double toler027 = 1.0000000000000006e-10;
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template<typename Ret, unsigned int Num>
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void
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test(const testcase_cyl_bessel_j<Ret> (&data)[Num], Ret toler)
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@ -748,5 +781,6 @@ main()
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test(data024, toler024);
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test(data025, toler025);
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test(data026, toler026);
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test(data027, toler027);
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return 0;
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}
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@ -742,6 +742,39 @@ data028[20] =
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};
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const double toler028 = 1.0000000000000006e-11;
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// Test data for nu=100.0000000000000000
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// max(|f - f_GSL|): 3.9022387751663778e-14 at index 16
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// max(|f - f_GSL| / |f_GSL|): 2.4760677072012703e-11
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// mean(f - f_GSL): 3.6878362466971231e-16
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// variance(f - f_GSL): 5.0707962306468580e-28
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// stddev(f - f_GSL): 2.2518428521206487e-14
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const testcase_cyl_neumann<double>
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data029[21] =
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{
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{ -2.2438688257729954e-02, 100.0000000000000000, 1000.0000000000000000, 0.0 },
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{ -2.1077595159819992e-02, 100.0000000000000000, 1100.0000000000000000, 0.0 },
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{ -3.5299439206692585e-03, 100.0000000000000000, 1200.0000000000000000, 0.0 },
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{ 1.4250019326536615e-02, 100.0000000000000000, 1300.0000000000000000, 0.0 },
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{ 2.1304679089735663e-02, 100.0000000000000000, 1400.0000000000000000, 0.0 },
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{ 1.5734395077905267e-02, 100.0000000000000000, 1500.0000000000000000, 0.0 },
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{ 2.5544633636137774e-03, 100.0000000000000000, 1600.0000000000000000, 0.0 },
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{ -1.0722045524849367e-02, 100.0000000000000000, 1700.0000000000000000, 0.0 },
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{ -1.8036919243226864e-02, 100.0000000000000000, 1800.0000000000000000, 0.0 },
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{ -1.6958415593079763e-02, 100.0000000000000000, 1900.0000000000000000, 0.0 },
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{ -8.8788704566276667e-03, 100.0000000000000000, 2000.0000000000000000, 0.0 },
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{ 2.2504407108413179e-03, 100.0000000000000000, 2100.0000000000000000, 0.0 },
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{ 1.1833215246712251e-02, 100.0000000000000000, 2200.0000000000000000, 0.0 },
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{ 1.6398784536343945e-02, 100.0000000000000000, 2300.0000000000000000, 0.0 },
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{ 1.4675984403642338e-02, 100.0000000000000000, 2400.0000000000000000, 0.0 },
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{ 7.7523920451654229e-03, 100.0000000000000000, 2500.0000000000000000, 0.0 },
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{ -1.5759822576003489e-03, 100.0000000000000000, 2600.0000000000000000, 0.0 },
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{ -9.9314877404787089e-03, 100.0000000000000000, 2700.0000000000000000, 0.0 },
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{ -1.4534495161704743e-02, 100.0000000000000000, 2800.0000000000000000, 0.0 },
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{ -1.4059273497237509e-02, 100.0000000000000000, 2900.0000000000000000, 0.0 },
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{ -8.9385158149605185e-03, 100.0000000000000000, 3000.0000000000000000, 0.0 },
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};
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const double toler029 = 1.0000000000000006e-10;
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template<typename Ret, unsigned int Num>
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void
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test(const testcase_cyl_neumann<Ret> (&data)[Num], Ret toler)
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@ -794,5 +827,6 @@ main()
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test(data026, toler026);
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test(data027, toler027);
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test(data028, toler028);
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test(data029, toler029);
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return 0;
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}
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@ -698,6 +698,39 @@ data026[21] =
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};
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const double toler026 = 1.0000000000000006e-11;
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// Test data for nu=100.0000000000000000
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// max(|f - f_GSL|): 3.9438938226332709e-14 at index 19
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// max(|f - f_GSL| / |f_GSL|): 2.0193411077170867e-11
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// mean(f - f_GSL): 1.6682360684660055e-15
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// variance(f - f_GSL): 5.3274331668346898e-28
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// stddev(f - f_GSL): 2.3081232997469372e-14
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const testcase_cyl_bessel_j<double>
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data027[21] =
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{
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{ 1.1676135007789573e-02, 100.0000000000000000, 1000.0000000000000000, 0.0 },
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{ -1.1699854778025796e-02, 100.0000000000000000, 1100.0000000000000000, 0.0 },
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{ -2.2801483405083697e-02, 100.0000000000000000, 1200.0000000000000000, 0.0 },
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{ -1.6973500787373915e-02, 100.0000000000000000, 1300.0000000000000000, 0.0 },
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{ -1.4154528803481308e-03, 100.0000000000000000, 1400.0000000000000000, 0.0 },
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{ 1.3333726584495232e-02, 100.0000000000000000, 1500.0000000000000000, 0.0 },
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{ 1.9802562020148559e-02, 100.0000000000000000, 1600.0000000000000000, 0.0 },
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{ 1.6129771279838816e-02, 100.0000000000000000, 1700.0000000000000000, 0.0 },
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{ 5.3753369281536031e-03, 100.0000000000000000, 1800.0000000000000000, 0.0 },
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{ -6.9238868725645785e-03, 100.0000000000000000, 1900.0000000000000000, 0.0 },
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{ -1.5487871720069789e-02, 100.0000000000000000, 2000.0000000000000000, 0.0 },
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{ -1.7275186717671070e-02, 100.0000000000000000, 2100.0000000000000000, 0.0 },
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{ -1.2233030525173150e-02, 100.0000000000000000, 2200.0000000000000000, 0.0 },
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{ -2.8518508672241900e-03, 100.0000000000000000, 2300.0000000000000000, 0.0 },
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{ 7.0784372270289329e-03, 100.0000000000000000, 2400.0000000000000000, 0.0 },
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{ 1.3955367586928166e-02, 100.0000000000000000, 2500.0000000000000000, 0.0 },
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{ 1.5574059842493392e-02, 100.0000000000000000, 2600.0000000000000000, 0.0 },
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{ 1.1718043044647556e-02, 100.0000000000000000, 2700.0000000000000000, 0.0 },
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{ 4.0320953231285607e-03, 100.0000000000000000, 2800.0000000000000000, 0.0 },
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{ -4.6895111783053977e-03, 100.0000000000000000, 2900.0000000000000000, 0.0 },
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{ -1.1507715400035966e-02, 100.0000000000000000, 3000.0000000000000000, 0.0 },
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};
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const double toler027 = 1.0000000000000006e-10;
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template<typename Ret, unsigned int Num>
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void
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test(const testcase_cyl_bessel_j<Ret> (&data)[Num], Ret toler)
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@ -748,5 +781,6 @@ main()
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test(data024, toler024);
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test(data025, toler025);
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test(data026, toler026);
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test(data027, toler027);
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return 0;
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}
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@ -742,6 +742,39 @@ data028[20] =
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};
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const double toler028 = 1.0000000000000006e-11;
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// Test data for nu=100.0000000000000000
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// max(|f - f_GSL|): 3.9022387751663778e-14 at index 16
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// max(|f - f_GSL| / |f_GSL|): 2.4760677072012703e-11
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// mean(f - f_GSL): 3.6878362466971231e-16
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// variance(f - f_GSL): 5.0707962306468580e-28
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// stddev(f - f_GSL): 2.2518428521206487e-14
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const testcase_cyl_neumann<double>
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data029[21] =
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{
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{ -2.2438688257729954e-02, 100.0000000000000000, 1000.0000000000000000, 0.0 },
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{ -2.1077595159819992e-02, 100.0000000000000000, 1100.0000000000000000, 0.0 },
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{ -3.5299439206692585e-03, 100.0000000000000000, 1200.0000000000000000, 0.0 },
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{ 1.4250019326536615e-02, 100.0000000000000000, 1300.0000000000000000, 0.0 },
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{ 2.1304679089735663e-02, 100.0000000000000000, 1400.0000000000000000, 0.0 },
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{ 1.5734395077905267e-02, 100.0000000000000000, 1500.0000000000000000, 0.0 },
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{ 2.5544633636137774e-03, 100.0000000000000000, 1600.0000000000000000, 0.0 },
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{ -1.0722045524849367e-02, 100.0000000000000000, 1700.0000000000000000, 0.0 },
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{ -1.8036919243226864e-02, 100.0000000000000000, 1800.0000000000000000, 0.0 },
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{ -1.6958415593079763e-02, 100.0000000000000000, 1900.0000000000000000, 0.0 },
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{ -8.8788704566276667e-03, 100.0000000000000000, 2000.0000000000000000, 0.0 },
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{ 2.2504407108413179e-03, 100.0000000000000000, 2100.0000000000000000, 0.0 },
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{ 1.1833215246712251e-02, 100.0000000000000000, 2200.0000000000000000, 0.0 },
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{ 1.6398784536343945e-02, 100.0000000000000000, 2300.0000000000000000, 0.0 },
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{ 1.4675984403642338e-02, 100.0000000000000000, 2400.0000000000000000, 0.0 },
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{ 7.7523920451654229e-03, 100.0000000000000000, 2500.0000000000000000, 0.0 },
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{ -1.5759822576003489e-03, 100.0000000000000000, 2600.0000000000000000, 0.0 },
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{ -9.9314877404787089e-03, 100.0000000000000000, 2700.0000000000000000, 0.0 },
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{ -1.4534495161704743e-02, 100.0000000000000000, 2800.0000000000000000, 0.0 },
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{ -1.4059273497237509e-02, 100.0000000000000000, 2900.0000000000000000, 0.0 },
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{ -8.9385158149605185e-03, 100.0000000000000000, 3000.0000000000000000, 0.0 },
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};
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const double toler029 = 1.0000000000000006e-10;
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template<typename Ret, unsigned int Num>
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void
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test(const testcase_cyl_neumann<Ret> (&data)[Num], Ret toler)
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@ -794,5 +827,6 @@ main()
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test(data026, toler026);
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test(data027, toler027);
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test(data028, toler028);
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test(data029, toler029);
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return 0;
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}
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