add floating point issues with constraints to manual and user's guide
Summary:
There are situations where our floating point operations have one behavior mathematically and another with floating point rounding, underflow, or overflow. We should document what this does and how to fix or trap the issue in simple cases.
For example, with a parameter declared with real<lower = 0> sigma, if the unconstrained value is high magnitude and negative (e.g., -500), then the constrained value will be 0 because exp(-500) underflows to 0.
Similarly, with real<lower = 0, upper = 1>, we'll get rounding to 1 for large-ish values of the parameter, even though mathematically, inverse logit should be strictly in (0, 1) (exclusive bounds).
See Aki's comment on the stan-dev/math issue for lub_constrain for more discussion.
Current Version:
v2.18.0