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


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 @@
  *  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
 //
@@ -358,16 +362,40 @@ 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) < 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();
(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.


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