[Bug-gsl] gsl_sf_bessel_Jn_e performance

[Jonny Taylor]

Hi All,

I don't know what the policy is regarding optimizations which  
(slightly) decrease code readability, but there's a simple change to  
the downward recurrence in gsl_sf_bessel_Jn_e which doubles the speed  
of the function (almost all the remaining time is spent in  
gsl_sf_bessel_J_CF1) for n of order 10-40.

The modified code is listed below.

Cheers
Jonny

      double twoInvX = 2.0 / x;
      double kf;
      for(k=n, kf=n; k>0; k--, kf--) {
        Jkm1 = kf*twoInvX * Jk - Jkp1;
        Jkp1 = Jk;
        Jk   = Jkm1;
      }