Possible infinite loop in Remez (from gforge #8867)
Imported issue: Initially reported by @chevilla in https://gforge.inria.fr/tracker/?group_id=1015&aid=8867
This is a hard case for Remez algorithm, but I am not completely sure that it should behave so badly. This behavior has to be checked.
verbosity=2!; b=round(pi,53,RD); p=remez(1,[|1,...,6|],[-1,b],1/sin(x));
Warning: the given expression is not a constant but an expression to evaluate. A faithful evaluation will be used.
Information: rounding down has happened.
Warning in Remez: a slower algorithm is used for this step
Performing an exchange step...
Warning in Remez: a slower algorithm is used for this step
Performing an exchange step...
Warning in Remez: a slower algorithm is used for this step
Performing an exchange step...
Warning in Remez: a slower algorithm is used for this step
Performing an exchange step...
Warning in Remez: a slower algorithm is used for this step
Performing an exchange step...
Warning in Remez: a slower algorithm is used for this step
Performing an exchange step...
Warning in Remez: a slower algorithm is used for this step
Performing an exchange step...
Information: 100 out of 501 points have been handled.
Information: 200 out of 501 points have been handled.
Information: 300 out of 501 points have been handled.
Information: 400 out of 501 points have been handled.
Information: 500 out of 501 points have been handled.
Warning: Remez algorithm failed (too many oscillations?)
Looping again
etc.