-- -----------------------------------------------------------------------------
-- approxRational
--- @approxRational@, applied to two real fractional numbers x and epsilon,
--- returns the simplest rational number within epsilon of x. A rational
--- number n%d in reduced form is said to be simpler than another n'%d' if
--- abs n <= abs n' && d <= d'. Any real interval contains a unique
--- simplest rational; here, for simplicity, we assume a closed rational
+-- | 'approxRational', applied to two real fractional numbers @x@ and @epsilon@,
+-- returns the simplest rational number within @epsilon@ of @x@.
+-- A rational number @y@ is said to be /simpler/ than another @y'@ if
+--
+-- * @'abs' ('numerator' y) <= 'abs' ('numerator' y')@, and
+--
+-- * @'denominator' y <= 'denominator' y'@.
+--
+-- Any real interval contains a unique simplest rational;
+-- in particular, note that @0\/1@ is the simplest rational of all.
+
+-- Implementation details: Here, for simplicity, we assume a closed rational
-- interval. If such an interval includes at least one whole number, then
-- the simplest rational is the absolutely least whole number. Otherwise,
-- the bounds are of the form q%1 + r%d and q%1 + r'%d', where abs r < d