+2018-11-18 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.
+
2018-11-17 Jonathan Wakely <jwakely@redhat.com>
Implement std::pmr::synchronized_pool_resource
* Do not attempt to use it directly. @headername{tr1/cmath}
*/
+/* __cyl_bessel_jn_asymp adapted from GNU GSL version 2.4 specfunc/bessel_j.c
+ * Copyright (C) 1996-2003 Gerard Jungman
+ */
+
//
// ISO C++ 14882 TR1: 5.2 Special functions
//
void
__cyl_bessel_jn_asymp(_Tp __nu, _Tp __x, _Tp & __Jnu, _Tp & __Nnu)
{
- const _Tp __mu = _Tp(4) * __nu * __nu;
- const _Tp __mum1 = __mu - _Tp(1);
- const _Tp __mum9 = __mu - _Tp(9);
- const _Tp __mum25 = __mu - _Tp(25);
- const _Tp __mum49 = __mu - _Tp(49);
- const _Tp __xx = _Tp(64) * __x * __x;
- const _Tp __P = _Tp(1) - __mum1 * __mum9 / (_Tp(2) * __xx)
- * (_Tp(1) - __mum25 * __mum49 / (_Tp(12) * __xx));
- const _Tp __Q = __mum1 / (_Tp(8) * __x)
- * (_Tp(1) - __mum9 * __mum25 / (_Tp(6) * __xx));
+ const _Tp __mu = _Tp(4) * __nu * __nu;
+ const _Tp __8x = _Tp(8) * __x;
+
+ _Tp __P = _Tp(0);
+ _Tp __Q = _Tp(0);
+
+ _Tp __k = _Tp(0);
+ _Tp __term = _Tp(1);
+
+ int __epsP = 0;
+ int __epsQ = 0;
+
+ _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+
+ do
+ {
+ __term *= (__k == 0
+ ? _Tp(1)
+ : -(__mu - (2 * __k - 1) * (2 * __k - 1)) / (__k * __8x));
+
+ __epsP = std::abs(__term) < __eps * std::abs(__P);
+ __P += __term;
+
+ __k++;
+
+ __term *= (__mu - (2 * __k - 1) * (2 * __k - 1)) / (__k * __8x);
+ __epsQ = std::abs(__term) < __eps * std::abs(__Q);
+ __Q += __term;
+
+ if (__epsP && __epsQ && __k > (__nu / 2.))
+ break;
+
+ __k++;
+ }
+ while (__k < 1000);
const _Tp __chi = __x - (__nu + _Tp(0.5L))
- * __numeric_constants<_Tp>::__pi_2();
+ * __numeric_constants<_Tp>::__pi_2();
+
const _Tp __c = std::cos(__chi);
const _Tp __s = std::sin(__chi);
const _Tp __coef = std::sqrt(_Tp(2)
/ (__numeric_constants<_Tp>::__pi() * __x));
+
__Jnu = __coef * (__c * __P - __s * __Q);
__Nnu = __coef * (__s * __P + __c * __Q);
};
const double toler026 = 1.0000000000000006e-11;
+// Test data for nu=100.0000000000000000
+// max(|f - f_GSL|): 3.9438938226332709e-14 at index 19
+// max(|f - f_GSL| / |f_GSL|): 2.0193411077170867e-11
+// mean(f - f_GSL): 1.6682360684660055e-15
+// variance(f - f_GSL): 5.3274331668346898e-28
+// stddev(f - f_GSL): 2.3081232997469372e-14
+const testcase_cyl_bessel_j<double>
+data027[21] =
+{
+ { 1.1676135007789573e-02, 100.0000000000000000, 1000.0000000000000000, 0.0 },
+ { -1.1699854778025796e-02, 100.0000000000000000, 1100.0000000000000000, 0.0 },
+ { -2.2801483405083697e-02, 100.0000000000000000, 1200.0000000000000000, 0.0 },
+ { -1.6973500787373915e-02, 100.0000000000000000, 1300.0000000000000000, 0.0 },
+ { -1.4154528803481308e-03, 100.0000000000000000, 1400.0000000000000000, 0.0 },
+ { 1.3333726584495232e-02, 100.0000000000000000, 1500.0000000000000000, 0.0 },
+ { 1.9802562020148559e-02, 100.0000000000000000, 1600.0000000000000000, 0.0 },
+ { 1.6129771279838816e-02, 100.0000000000000000, 1700.0000000000000000, 0.0 },
+ { 5.3753369281536031e-03, 100.0000000000000000, 1800.0000000000000000, 0.0 },
+ { -6.9238868725645785e-03, 100.0000000000000000, 1900.0000000000000000, 0.0 },
+ { -1.5487871720069789e-02, 100.0000000000000000, 2000.0000000000000000, 0.0 },
+ { -1.7275186717671070e-02, 100.0000000000000000, 2100.0000000000000000, 0.0 },
+ { -1.2233030525173150e-02, 100.0000000000000000, 2200.0000000000000000, 0.0 },
+ { -2.8518508672241900e-03, 100.0000000000000000, 2300.0000000000000000, 0.0 },
+ { 7.0784372270289329e-03, 100.0000000000000000, 2400.0000000000000000, 0.0 },
+ { 1.3955367586928166e-02, 100.0000000000000000, 2500.0000000000000000, 0.0 },
+ { 1.5574059842493392e-02, 100.0000000000000000, 2600.0000000000000000, 0.0 },
+ { 1.1718043044647556e-02, 100.0000000000000000, 2700.0000000000000000, 0.0 },
+ { 4.0320953231285607e-03, 100.0000000000000000, 2800.0000000000000000, 0.0 },
+ { -4.6895111783053977e-03, 100.0000000000000000, 2900.0000000000000000, 0.0 },
+ { -1.1507715400035966e-02, 100.0000000000000000, 3000.0000000000000000, 0.0 },
+};
+const double toler027 = 1.0000000000000006e-10;
+
template<typename Ret, unsigned int Num>
void
test(const testcase_cyl_bessel_j<Ret> (&data)[Num], Ret toler)
test(data024, toler024);
test(data025, toler025);
test(data026, toler026);
+ test(data027, toler027);
return 0;
}
};
const double toler028 = 1.0000000000000006e-11;
+// Test data for nu=100.0000000000000000
+// max(|f - f_GSL|): 3.9022387751663778e-14 at index 16
+// max(|f - f_GSL| / |f_GSL|): 2.4760677072012703e-11
+// mean(f - f_GSL): 3.6878362466971231e-16
+// variance(f - f_GSL): 5.0707962306468580e-28
+// stddev(f - f_GSL): 2.2518428521206487e-14
+const testcase_cyl_neumann<double>
+data029[21] =
+{
+ { -2.2438688257729954e-02, 100.0000000000000000, 1000.0000000000000000, 0.0 },
+ { -2.1077595159819992e-02, 100.0000000000000000, 1100.0000000000000000, 0.0 },
+ { -3.5299439206692585e-03, 100.0000000000000000, 1200.0000000000000000, 0.0 },
+ { 1.4250019326536615e-02, 100.0000000000000000, 1300.0000000000000000, 0.0 },
+ { 2.1304679089735663e-02, 100.0000000000000000, 1400.0000000000000000, 0.0 },
+ { 1.5734395077905267e-02, 100.0000000000000000, 1500.0000000000000000, 0.0 },
+ { 2.5544633636137774e-03, 100.0000000000000000, 1600.0000000000000000, 0.0 },
+ { -1.0722045524849367e-02, 100.0000000000000000, 1700.0000000000000000, 0.0 },
+ { -1.8036919243226864e-02, 100.0000000000000000, 1800.0000000000000000, 0.0 },
+ { -1.6958415593079763e-02, 100.0000000000000000, 1900.0000000000000000, 0.0 },
+ { -8.8788704566276667e-03, 100.0000000000000000, 2000.0000000000000000, 0.0 },
+ { 2.2504407108413179e-03, 100.0000000000000000, 2100.0000000000000000, 0.0 },
+ { 1.1833215246712251e-02, 100.0000000000000000, 2200.0000000000000000, 0.0 },
+ { 1.6398784536343945e-02, 100.0000000000000000, 2300.0000000000000000, 0.0 },
+ { 1.4675984403642338e-02, 100.0000000000000000, 2400.0000000000000000, 0.0 },
+ { 7.7523920451654229e-03, 100.0000000000000000, 2500.0000000000000000, 0.0 },
+ { -1.5759822576003489e-03, 100.0000000000000000, 2600.0000000000000000, 0.0 },
+ { -9.9314877404787089e-03, 100.0000000000000000, 2700.0000000000000000, 0.0 },
+ { -1.4534495161704743e-02, 100.0000000000000000, 2800.0000000000000000, 0.0 },
+ { -1.4059273497237509e-02, 100.0000000000000000, 2900.0000000000000000, 0.0 },
+ { -8.9385158149605185e-03, 100.0000000000000000, 3000.0000000000000000, 0.0 },
+};
+const double toler029 = 1.0000000000000006e-10;
+
template<typename Ret, unsigned int Num>
void
test(const testcase_cyl_neumann<Ret> (&data)[Num], Ret toler)
test(data026, toler026);
test(data027, toler027);
test(data028, toler028);
+ test(data029, toler029);
return 0;
}
};
const double toler026 = 1.0000000000000006e-11;
+// Test data for nu=100.0000000000000000
+// max(|f - f_GSL|): 3.9438938226332709e-14 at index 19
+// max(|f - f_GSL| / |f_GSL|): 2.0193411077170867e-11
+// mean(f - f_GSL): 1.6682360684660055e-15
+// variance(f - f_GSL): 5.3274331668346898e-28
+// stddev(f - f_GSL): 2.3081232997469372e-14
+const testcase_cyl_bessel_j<double>
+data027[21] =
+{
+ { 1.1676135007789573e-02, 100.0000000000000000, 1000.0000000000000000, 0.0 },
+ { -1.1699854778025796e-02, 100.0000000000000000, 1100.0000000000000000, 0.0 },
+ { -2.2801483405083697e-02, 100.0000000000000000, 1200.0000000000000000, 0.0 },
+ { -1.6973500787373915e-02, 100.0000000000000000, 1300.0000000000000000, 0.0 },
+ { -1.4154528803481308e-03, 100.0000000000000000, 1400.0000000000000000, 0.0 },
+ { 1.3333726584495232e-02, 100.0000000000000000, 1500.0000000000000000, 0.0 },
+ { 1.9802562020148559e-02, 100.0000000000000000, 1600.0000000000000000, 0.0 },
+ { 1.6129771279838816e-02, 100.0000000000000000, 1700.0000000000000000, 0.0 },
+ { 5.3753369281536031e-03, 100.0000000000000000, 1800.0000000000000000, 0.0 },
+ { -6.9238868725645785e-03, 100.0000000000000000, 1900.0000000000000000, 0.0 },
+ { -1.5487871720069789e-02, 100.0000000000000000, 2000.0000000000000000, 0.0 },
+ { -1.7275186717671070e-02, 100.0000000000000000, 2100.0000000000000000, 0.0 },
+ { -1.2233030525173150e-02, 100.0000000000000000, 2200.0000000000000000, 0.0 },
+ { -2.8518508672241900e-03, 100.0000000000000000, 2300.0000000000000000, 0.0 },
+ { 7.0784372270289329e-03, 100.0000000000000000, 2400.0000000000000000, 0.0 },
+ { 1.3955367586928166e-02, 100.0000000000000000, 2500.0000000000000000, 0.0 },
+ { 1.5574059842493392e-02, 100.0000000000000000, 2600.0000000000000000, 0.0 },
+ { 1.1718043044647556e-02, 100.0000000000000000, 2700.0000000000000000, 0.0 },
+ { 4.0320953231285607e-03, 100.0000000000000000, 2800.0000000000000000, 0.0 },
+ { -4.6895111783053977e-03, 100.0000000000000000, 2900.0000000000000000, 0.0 },
+ { -1.1507715400035966e-02, 100.0000000000000000, 3000.0000000000000000, 0.0 },
+};
+const double toler027 = 1.0000000000000006e-10;
+
template<typename Ret, unsigned int Num>
void
test(const testcase_cyl_bessel_j<Ret> (&data)[Num], Ret toler)
test(data024, toler024);
test(data025, toler025);
test(data026, toler026);
+ test(data027, toler027);
return 0;
}
};
const double toler028 = 1.0000000000000006e-11;
+// Test data for nu=100.0000000000000000
+// max(|f - f_GSL|): 3.9022387751663778e-14 at index 16
+// max(|f - f_GSL| / |f_GSL|): 2.4760677072012703e-11
+// mean(f - f_GSL): 3.6878362466971231e-16
+// variance(f - f_GSL): 5.0707962306468580e-28
+// stddev(f - f_GSL): 2.2518428521206487e-14
+const testcase_cyl_neumann<double>
+data029[21] =
+{
+ { -2.2438688257729954e-02, 100.0000000000000000, 1000.0000000000000000, 0.0 },
+ { -2.1077595159819992e-02, 100.0000000000000000, 1100.0000000000000000, 0.0 },
+ { -3.5299439206692585e-03, 100.0000000000000000, 1200.0000000000000000, 0.0 },
+ { 1.4250019326536615e-02, 100.0000000000000000, 1300.0000000000000000, 0.0 },
+ { 2.1304679089735663e-02, 100.0000000000000000, 1400.0000000000000000, 0.0 },
+ { 1.5734395077905267e-02, 100.0000000000000000, 1500.0000000000000000, 0.0 },
+ { 2.5544633636137774e-03, 100.0000000000000000, 1600.0000000000000000, 0.0 },
+ { -1.0722045524849367e-02, 100.0000000000000000, 1700.0000000000000000, 0.0 },
+ { -1.8036919243226864e-02, 100.0000000000000000, 1800.0000000000000000, 0.0 },
+ { -1.6958415593079763e-02, 100.0000000000000000, 1900.0000000000000000, 0.0 },
+ { -8.8788704566276667e-03, 100.0000000000000000, 2000.0000000000000000, 0.0 },
+ { 2.2504407108413179e-03, 100.0000000000000000, 2100.0000000000000000, 0.0 },
+ { 1.1833215246712251e-02, 100.0000000000000000, 2200.0000000000000000, 0.0 },
+ { 1.6398784536343945e-02, 100.0000000000000000, 2300.0000000000000000, 0.0 },
+ { 1.4675984403642338e-02, 100.0000000000000000, 2400.0000000000000000, 0.0 },
+ { 7.7523920451654229e-03, 100.0000000000000000, 2500.0000000000000000, 0.0 },
+ { -1.5759822576003489e-03, 100.0000000000000000, 2600.0000000000000000, 0.0 },
+ { -9.9314877404787089e-03, 100.0000000000000000, 2700.0000000000000000, 0.0 },
+ { -1.4534495161704743e-02, 100.0000000000000000, 2800.0000000000000000, 0.0 },
+ { -1.4059273497237509e-02, 100.0000000000000000, 2900.0000000000000000, 0.0 },
+ { -8.9385158149605185e-03, 100.0000000000000000, 3000.0000000000000000, 0.0 },
+};
+const double toler029 = 1.0000000000000006e-10;
+
template<typename Ret, unsigned int Num>
void
test(const testcase_cyl_neumann<Ret> (&data)[Num], Ret toler)
test(data026, toler026);
test(data027, toler027);
test(data028, toler028);
+ test(data029, toler029);
return 0;
}
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