And the test cases
diff --git
a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc
b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc
index 26f4dd3..e340b78 100644
---
a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc
+++
b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc
@@ -698,6 +698,26 @@ data026[21] =
};
const double toler026 = 1.0000000000000006e-11;
+// Test data for nu=100.00000000000000.
+// max(|f - f_GSL|): 2.5857788132910287e-14
+// max(|f - f_GSL| / |f_GSL|): 1.6767662425535933e-11
+const testcase_cyl_bessel_j<double>
+data027[11] =
+{
+ { 0.0116761350077845, 100.0000000000000000, 1000.0000000000000000 },
+ {-0.0116998547780258, 100.0000000000000000, 1100.0000000000000000 },
+ {-0.0228014834050837, 100.0000000000000000, 1200.0000000000000000 },
+ {-0.0169735007873739, 100.0000000000000000, 1300.0000000000000000 },
+ {-0.0014154528803530, 100.0000000000000000, 1400.0000000000000000 },
+ { 0.0133337265844988, 100.0000000000000000, 1500.0000000000000000 },
+ { 0.0198025620201474, 100.0000000000000000, 1600.0000000000000000 },
+ { 0.0161297712798388, 100.0000000000000000, 1700.0000000000000000 },
+ { 0.0053753369281577, 100.0000000000000000, 1800.0000000000000000 },
+ {-0.0069238868725646, 100.0000000000000000, 1900.0000000000000000 },
+ {-0.0154878717200738, 100.0000000000000000, 2000.0000000000000000 },
+};
+const double toler027 = 1.0000000000000006e-10;
+
template<typename Ret, unsigned int Num>
void
test(const testcase_cyl_bessel_j<Ret> (&data)[Num], Ret toler)
@@ -748,5 +768,6 @@ main()
test(data024, toler024);
test(data025, toler025);
test(data026, toler026);
+ test(data027, toler027);
return 0;
}
diff --git
a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc
b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc
index 5579149..957aacd 100644
---
a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc
+++
b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc
@@ -742,6 +742,26 @@ data028[20] =
};
const double toler028 = 1.0000000000000006e-11;
+// Test data for nu=100.00000000000000.
+// max(|f - f_GSL|): 3.1049815496508870e-14
+// max(|f - f_GSL| / |f_GSL|): 8.4272302674970308e-12
+const testcase_cyl_neumann<double>
+data029[11] =
+{
+ {-0.0224386882577326, 100.0000000000000000, 1000.0000000000000000 },
+ {-0.0210775951598200, 100.0000000000000000, 1100.0000000000000000 },
+ {-0.0035299439206693, 100.0000000000000000, 1200.0000000000000000 },
+ { 0.0142500193265366, 100.0000000000000000, 1300.0000000000000000 },
+ { 0.0213046790897353, 100.0000000000000000, 1400.0000000000000000 },
+ { 0.0157343950779022, 100.0000000000000000, 1500.0000000000000000 },
+ { 0.0025544633636228, 100.0000000000000000, 1600.0000000000000000 },
+ {-0.0107220455248494, 100.0000000000000000, 1700.0000000000000000 },
+ {-0.0180369192432256, 100.0000000000000000, 1800.0000000000000000 },
+ {-0.0169584155930798, 100.0000000000000000, 1900.0000000000000000 },
+ {-0.0088788704566206, 100.0000000000000000, 2000.0000000000000000 },
+};
+const double toler029 = 1.0000000000000006e-11;
+
template<typename Ret, unsigned int Num>
void
test(const testcase_cyl_neumann<Ret> (&data)[Num], Ret toler)
@@ -794,5 +814,6 @@ main()
test(data026, toler026);
test(data027, toler027);
test(data028, toler028);
+ test(data029, toler029);
return 0;
}
On 01/04/2018 09:54 PM, Michele Pezzutti wrote:
On 01/04/2018 06:16 PM, Ed Smith-Rowland wrote:
I've seen their implementation. It's tight. Feel free to port it.
I assume this is it:
int
gsl_sf_bessel_Jnu_asympx_e(const double nu, const double x,
gsl_sf_result * result);
You do want to give Q or b one more term so as to make that last
factor as small as possible. They're right.
Here it is.
diff --git a/libstdc++-v3/include/tr1/bessel_function.tcc
b/libstdc++-v3/include/tr1/bessel_function.tcc
index 7ac733d..7842350 100644
--- a/libstdc++-v3/include/tr1/bessel_function.tcc
+++ b/libstdc++-v3/include/tr1/bessel_function.tcc
@@ -353,21 +353,47 @@ namespace tr1
* @param __x The argument of the Bessel functions.
* @param __Jnu The output Bessel function of the first kind.
* @param __Nnu The output Neumann function (Bessel function
of the second kind).
+ *
+ * Adapted for libstdc++ from GNU GSL version 2.4
specfunc/bessel_j.c
+ * Copyright (C) 1996,1997,1998,1999,2000,2001,2002,2003 Gerard
Jungman
*/
template <typename _Tp>
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 __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) < std::abs(__eps * __P);
+ __P += __term;
+
+ k++;
+
+ __term *= (__mu - (2 * k - 1) * (2 * k - 1)) / (k * __8x);
+ __epsQ = std::abs(__term) < std::abs(__eps * __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();
In principal, these ideas should be ported to I,K but I think (and
IIRC GSL agrees) these under,over-flow before they have much effect.
I think I put the full series in there. They could use a similar
clean-up.
But let's get this in there first.
Ed
