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The truncnorm distribution has two numerical problems. The first problem is that it cannot deal at all with extreme tails, such as x=1000. The second problem is that its implementation does not use the symmetry of the normal distribution as much as it could, resulting in higher precision for negative tails where the cdf is near epsilon, and lower precision for positive tails where the cdf is near 1-epsilon. This is related to pv's comment #2477 (comment).
This PR addresses only the second of these two problems. It should close or partially close the issues #1489 and #2477.