decball_mid, decball_rad, decball_shell, decball_lower, decball_upper, decball_abs_lower, decball_abs_upper, decball_add_rad, decball_set_interval

Components and bounds of a ball x = [m \pm r], as balls. mid gives the exact ball m and rad the exact ball r (midpoints and radii are always representable), and shell gives [0 \pm r]. lower and upper give the endpoints m - r and m + r rounded to the context precision toward -\infty and +\infty respectively, and abs_lower and abs_upper give lower and upper bounds for |x| (\max(|m| - r, 0) rounded toward zero and |m| + r rounded up), all as exact balls, so that the results enclose the true bounds. An infinite radius gives GR_DOMAIN (the endpoints are not real numbers) except for abs_lower, which gives zero, and rad, which cannot represent an infinite radius as a ball. add_rad sets res to [x \pm |r|] (the same as set_interval_mid_rad), and set_interval sets res to the smallest ball containing both lo and hi (their convex hull, in either order), with the midpoint rounded to the context precision.