Hi.
This patch intends to fix Bug 83566 - cyl_bessel_j returns wrong result
for x>1000 for high orders.
See https://gcc.gnu.org/bugzilla/show_bug.cgi?id=83566 for issue
description.
* libstdc++-v3/include/tr1/bessel_function.tcc
Series expansion in __cyl_bessel_jn_asymp() shall not be
truncated at the first terms.
At least nu/2 terms shall be added, in order to have a guaranteed
error bound.
*
libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc
Testcase for x > 1000 added.
*
libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc
Testcase for x > 1000 added.
*
libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc
Testcase for x > 1000 added.
*
libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc
Testcase for x > 1000 added.
diff --git a/libstdc++-v3/include/tr1/bessel_function.tcc
b/libstdc++-v3/include/tr1/bessel_function.tcc
index 26c66cabe29..7b94b84a6ea 100644
--- a/libstdc++-v3/include/tr1/bessel_function.tcc
+++ b/libstdc++-v3/include/tr1/bessel_function.tcc
@@ -27,6 +27,10 @@
* 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
//
@@ -358,24 +362,51 @@ namespace tr1
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);
diff --git
a/libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc
b/libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc
index 475c6dcaa4a..7900af3c959 100644
---
a/libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc
+++
b/libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc
@@ -698,6 +698,39 @@ data026[21] =
};
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)
@@ -748,5 +781,6 @@ main()
test(data024, toler024);
test(data025, toler025);
test(data026, toler026);
+ test(data027, toler027);
return 0;
}
diff --git
a/libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc
b/libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc
index da1250278d5..835ce8cd676 100644
--- a/libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc
+++ b/libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc
@@ -742,6 +742,39 @@ data028[20] =
};
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)
@@ -794,5 +827,6 @@ main()
test(data026, toler026);
test(data027, toler027);
test(data028, toler028);
+ test(data029, toler029);
return 0;
}
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 06a2d192df0..ee587cbad86 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 +698,39 @@ data026[21] =
};
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)
@@ -748,5 +781,6 @@ 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 3c0cbe7b977..d73f6a604fe 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 +742,39 @@ data028[20] =
};
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)
@@ -794,5 +827,6 @@ main()
test(data026, toler026);
test(data027, toler027);
test(data028, toler028);
+ test(data029, toler029);
return 0;
}
Regards
Michele
On 06/05/2018 17:56, Ed Smith-Rowland wrote:
Michele,
So I think the patch you had plus tests
testsuite/tr1/5_numerical_facilities/special_functions/09_cyl_bessel_j/check_value.cc
testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc
plus I'd like the new tests also in
testsuite/special_functions/08_cyl_bessel_j/check_value.cc
testsuite/special_functions/10_cyl_neumann/check_value.cc
for C++17.
Put that up with a Changelog and see if we're all good.
Thank you for going through this and other math issues.
Ed
