Fix Bug 83566 - cyl_bessel_j returns wrong result for x>1000 for high orders

[Michele Pezzutti]

On 01/05/2018 05:50 PM, Jonathan Wakely wrote:
> On 05/01/18 09:54 -0500, Ed Smith-Rowland wrote:
>> This looks good to me.  The only nit is that you have to uglify the k 
>> loop variable.
>
> Right, it needs to be __k.
>
> I'm also not sure we can put the copyright notice there, rather than
> at the top of the file. We can collapse the years to 1996-2003 so I
> suggest adding to the top of the file something like:
>
> /* __cyl_bessel_jn_asymp adapted from GNU GSL version 2.4 
> specfunc/bessel_j.c
> * Copyright (C) 1996-2003 Gerard Jungman
> */
>
diff --git a/libstdc++-v3/include/tr1/bessel_function.tcc 
b/libstdc++-v3/include/tr1/bessel_function.tcc
index 7ac733d..6f5ff34 100644
--- a/libstdc++-v3/include/tr1/bessel_function.tcc
+++ b/libstdc++-v3/include/tr1/bessel_function.tcc
@@ -27,6 +27,10 @@
 Â  *Â  Do not attempt to use it directly. @headername{tr1/cmath}
 Â  */

+/* __cyl_bessel_jn_asymp adapted from GNU GSL version 2.4 
specfunc/bessel_j.c
+ * Copyright (C) 1996-2003 Gerard Jungman
+ */
+
 Â //
 Â // ISO C++ 14882 TR1: 5.2Â  Special functions
 Â //
@@ -358,16 +362,40 @@ namespace tr1
 Â Â Â Â  void
 Â Â Â Â  __cyl_bessel_jn_asymp(_Tp __nu, _Tp __x, _Tp & __Jnu, _Tp & __Nnu)
 Â Â Â Â  {
-      const _Tp __mu   = _Tp(4) * __nu * __nu;
-Â Â Â Â Â  const _Tp __mum1 = __mu - _Tp(1);
-Â Â Â Â Â  const _Tp __mum9 = __mu - _Tp(9);
-Â Â Â Â Â  const _Tp __mum25 = __mu - _Tp(25);
-Â Â Â Â Â  const _Tp __mum49 = __mu - _Tp(49);
-Â Â Â Â Â  const _Tp __xx = _Tp(64) * __x * __x;
-Â Â Â Â Â  const _Tp __P = _Tp(1) - __mum1 * __mum9 / (_Tp(2) * __xx)
-Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  * (_Tp(1) - __mum25 * __mum49 / (_Tp(12) * __xx));
-Â Â Â Â Â  const _Tp __Q = __mum1 / (_Tp(8) * __x)
-Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  * (_Tp(1) - __mum9 * __mum25 / (_Tp(6) * __xx));
+Â Â Â Â Â  const _Tp __mu = _Tp(4) * __nu * __nu;
+Â Â Â Â Â  const _Tp __8x = _Tp(8) * __x;
+
+Â Â Â Â Â  _Tp __P = _Tp(0);
+Â Â Â Â Â  _Tp __Q = _Tp(0);
+
+Â Â Â Â Â  _Tp __k = _Tp(0);
+Â Â Â Â Â  _Tp __term = _Tp(1);
+
+Â Â Â Â Â  int __epsP = 0;
+Â Â Â Â Â  int __epsQ = 0;
+
+Â Â Â Â Â  _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+
+Â Â Â Â Â  do
+Â Â Â Â Â Â Â  {
+Â Â Â Â Â Â Â Â Â  __term *= (__k == 0) ? _Tp(1) : -(__mu - (2 * __k - 1) * (2 * 
__k - 1))
+Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  / (__k * __8x);
+Â Â Â Â Â Â Â Â Â  __epsP = std::abs(__term) < std::abs(__eps * __P);
+Â Â Â Â Â Â Â Â Â  __P += __term;
+
+Â Â Â Â Â Â Â Â Â  __k++;
+
+Â Â Â Â Â Â Â Â Â  __term *= (__mu - (2 * __k - 1) * (2 * __k - 1)) / (__k * __8x);
+Â Â Â Â Â Â Â Â Â  __epsQ = std::abs(__term) < std::abs(__eps * __Q);
+Â Â Â Â Â Â Â Â Â  __Q += __term;
+
+Â Â Â Â Â Â Â Â Â  if (__epsP && __epsQ && __k > __nu / 2.)
+Â Â Â Â Â Â Â Â Â Â Â  break;
+
+Â Â Â Â Â Â Â Â Â  __k++;
+Â Â Â Â Â Â Â  }
+Â Â Â Â Â  while (__k < 1000);
+

 Â Â Â Â Â Â  const _Tp __chi = __x - (__nu + _Tp(0.5L))
 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  * __numeric_constants<_Tp>::__pi_2();
>> (I hope we can un-uglify our variables when modules come!)
>>
>> Do you have copyright assignment in place and all that?
>
> That appears to be underway.
No news since I sent questionnaire though.

>
> Thanks for working on this.
>
Welcome.