[ParadaCarleton]

When the step size shrinks below the floating-point resolution of the current point, PALC's corrector can converge to a point equal to the current one in every coordinate, and the Secant tangent through the two equal points is 0/0, so the next tangent and predictor are NaN. This makes corrector! refuse such a step for a Secant tangent and set stopcontinuation, so the branch ends at the last point it moved to with a finite tangent and predictor (stalled_step). A Bordered tangent is computed at one point and stays defined, so it keeps its current behaviour. The added test in test/continuation/palc_secant_stall.jl refuses every corrector past λ = 1/2 with dsmin = floatmin(Float32) and checks that the continuation stops below 1/2 with a finite tangent and predictor.

[rveltz]

Hi

I agree with this but I never saw that in practice. How did you come up with this?

I'd be happy to merge but the only point is the test new.u == current.u which in big dimension seems a lot to ask. The corrector would fail anyway so why adding this?

[ParadaCarleton]

I agree with this but I never saw that in practice. How did you come up with this?

Result of #356 (setting dsmin to floatmin, so when the step size gets very small it can underflow). No longer practically relevant since I closed that suggestion, but nothing wrong with fixing it anyway I suppose.